Muller marked his 400th top-flight outing for Bayern with the opening goal after seven minutes at the Allianz Arena, before the Germany international teed up Dayot Upamecano for a second after the interval.
Leroy Sane added a third for Julian Nagelsmann's side and Lewandowski was able to find a record 43rd league goal in 2021 to surpass Bayern legend's Gerd Muller's long-standing Bundesliga calendar-year scoring record as the hosts cruised to victory.
Leaders Bayern hold a nine-point advantage at the summit, with Dortmund – who play Hertha Berlin on Saturday – sat in second heading into the mid-season break.
Bayern were soon ahead when Muller poked home from close range after Koen Casteels had parried Serge Gnabry's strike, before Manuel Neuer thwarted Wout Weghorst at the other end.
Jamal Musiala almost doubled Bayern's lead but dragged wide, while Casteels denied Lewandowski's header from point-blank range.
Muller delicately chipped for Upamecano to head into the bottom-left corner after the interval, with Sane expertly curling in via the left post just two minutes later.
Lewandowski then had two opportunities to break Gerd Muller's benchmark, but wastefully prodded over with the first before an excellent Casteels save denied him from the second.
The Poland striker eventually managed his landmark finish when Musiala selflessly headed across goal for the Poland striker to volley in as Bayern eased to victory.
What does it mean? Bayern title favourites again heading into mid-season break
Bayern, who have not lost any of their last 25 home league matches against Wolfsburg, once again head into the mid-season break top of the Bundesliga – this time leading by at least six points, with Dortmund set to play their game in hand against Hertha Berlin on Saturday.
In the three points-per-win era, the Bavarians have won the title in 14 of the 15 seasons when they have been at the summit at the halfway point. By contrast, Wolfsburg have now lost seven consecutive competitive matches.
Gnabry the Great
Muller and Lewandowski seemingly steal the plaudits most weeks, but Gnabry's dominant performance should not go under the radar.
The Germany winger not only provided an assist but also laid on a team-leading three chances – along with full-back Alphonso Davies and Musiala – as he ensured a torrid game for Yannick Gerhardt at left wing-back.
Woeful Weghorst
Weghorst wasted a glorious opportunity to equalise immediately after Muller's opener and that set the tone for a frustrating performance from the striker.
The Netherlands international cut an isolated figure up top, winning just over a third of his 14 duels, while relinquishing possession a team-high 18 times.
What's next?
The Bundesliga now takes a break until 2022. Bayern return to action at home to Borussia Monchengladbach on January 7, while Wolfsburg visit Bochum two days later.
Vincent Kompany's side, who suffered a 1-0 cup defeat to Bayer Leverkusen on Tuesday, were without the injured Harry Kane, Manuel Neuer and Serge Gnabry for the home contest.
And the Bavarians got off to a good start when an unmarked Dayot Upamecano headed in the opener in the 19th minute.
But Upamecano's defensive error five minutes into the second half allowed Mathias Honsak to latch on to his poor back pass and fire past Daniel Peretz to make it 1-1.
However, Musiala, introduced straight after that goal, took just five minutes to make an impact as the 21-year-old's low drive from the edge of the box restored Bayern's lead.
Another Bayern substitute, Leon Goretzka, then added a third with a deflected shot in the 84th minute before Heidenheim pulled a goal back through a Niclas Doresch tap-in.
Musiala then settled the nerves for the hosts as he ran onto a through ball from his own half before scoring in the stoppage time to make it 4-2 with his eighth league goal of the season.
The result sees Bayern extend their lead at the top to six points over second-placed Eintracht Frankfurt, while Heidenheim remain in 16th place.
Data Debrief: Bayern can't stop scoring
Bayern Munich have now scored in each of their last 20 games in the Bundesliga, scoring an incredible 57 goals during that run.
They are also the only side to have scored in each of the 13 games in the German top-flight this season.
Kompany's side, who are unbeaten after 13 games in the Bundesliga, have now matched their last joint longest unbeaten streak, which ran from May 2023 to November 2023.
Heidenheim, meanwhile, have lost five games on the trot now - their longest losing streak in the league since at least the 2004/2005 season.
The German and European champions' 32-game unbeaten streak was ended in a shock 4-1 loss at Hoffenheim last weekend and they nearly dropped two more points on Sunday.
Lewandowski had put Bayern two goals in front - the second assisted by full debutant Chris Richards - but Jhon Cordoba powered in a header with almost an hour played and Matheus Cunha scored an impressive equaliser soon after.
The prolific striker's hat-trick goal was then instantly cancelled out by Jessic Ngankam in an incredible second half, but Lewandowski won a penalty in stoppage time that he stepped up to convert as Bayern got back to winning ways in the league.
In the latest instalment of his one-sided battle with defenders in the German top flight, it was a familiar story as Lewandowski came out on top, taking his haul to a startling 10 goals in five matches this season.
That is a Bundesliga record for this stage of the season, and last season's haul of 34 goals must already be in his sights after a perfect hat-trick.
Three days after Bayern beat Atletico Madrid 4-0 in the Champions League - a match in which Lewandowski left the scoring to others - the German champions were again irresistible at their Allianz Arena home. There was even a goal for 17-year-old substitute Jamal Musiala in the closing moments, to cap a fine team performance.
Lewandowski gave Bayern a 10th-minute lead, collecting a neat pass from the marauding Kingsley Coman and firing left-footed, low into the bottom right corner.
Although Eintracht had their moments, Bayern had Lewandowski. It was 2-0 in the 26th minute with the Poland striker again the scorer, this time producing a deft header from a right-wing corner, connecting near the penalty spot and sending the ball inside the left post.
He could not capitalise on chances to make it a first-half treble but the hat-trick was complete after an hour.
Douglas Costa's throughball was taken neatly in his stride by Lewandowski and, as two defenders converged, he found just enough time to adjust his feet and send a low shot wide of Kevin Trapp and into the right corner.
Bayern suffered an early setback when Alphonso Davies went down off the ball, clutching his ankle. His replacement, Lucas Hernandez, should have made it 4-0 but shot wastefully over from close range after being picked out by Coman.
The fourth soon came though and it was a super strike from Sane, cutting in from the right and curling an unstoppable 25-yard shot past Trapp. Musiala bundled the fifth with the last kick of the match.
What does it mean?
Eintracht were on an eight-match unbeaten run heading into this game, including their opening four of this Bundesliga campaign. But against the might of Bayern they were reduced to cannon fodder.
Bayern’s defeat to Hoffenheim four weeks ago could look terribly anomalous this season, because this was another performance that suggested it will be a procession to the title for Hansi Flick’s team.
Lethal Lewy
Five shots, four on target, three goals. Lewandowski makes goalscoring look terribly easy at times. Each finish was immaculate, and on this form, Gerd Muller’s record of 40 goals in a Bundesliga season will come under threat. He only had 31 touches in the entire game, but he is the man with the golden touch.
The defence rests
Eintracht’s back three simply were incapable of getting near enough to the man they knew they had to keep under wraps. Makoto Hasebe, at the heart of the backline, made just two tackles all day, and the way Lewandowski took a mile whenever he was given an inch reflected badly on the defensive unit.
Generous defending is hardly a new phenomenon in this fixture: Bayern had won each of their previous 12 competitive home games against Frankfurt, and by an aggregate 40-7 scoreline.
What's next?
Bayern are back on Champions League duty as they face Lokomotiv Moscow on Tuesday. Eintracht will welcome Werder Bremen in the Bundesliga next Saturday.
In the latest instalment of his one-sided battle with defenders in the German top flight, it was a familiar story as Lewandowski came out on top, taking his haul to a startling 10 goals in five matches this season.
That is a Bundesliga record for this stage of the season, and last season's haul of 34 goals must already be in his sights after a perfect hat-trick.
Three days after Bayern beat Atletico Madrid 4-0 in the Champions League - a match in which Lewandowski left the scoring to others - the German champions were again irresistible at their Allianz Arena home. There was even a goal for 17-year-old substitute Jamal Musiala in the closing moments, to cap a fine team performance.
Lewandowski gave Bayern a 10th-minute lead, collecting a neat pass from the marauding Kingsley Coman and firing left-footed, low into the bottom right corner.
Although Eintracht had their moments, Bayern had Lewandowski. It was 2-0 in the 26th minute with the Poland striker again the scorer, this time producing a deft header from a right-wing corner, connecting near the penalty spot and sending the ball inside the left post.
He could not capitalise on chances to make it a first-half treble but the hat-trick was complete after an hour.
Douglas Costa's throughball was taken neatly in his stride by Lewandowski and, as two defenders converged, he found just enough time to adjust his feet and send a low shot wide of Kevin Trapp and into the right corner.
Bayern suffered an early setback when Alphonso Davies went down off the ball, clutching his ankle. His replacement, Lucas Hernandez, should have made it 4-0 but shot wastefully over from close range after being picked out by Coman.
The fourth soon came though and it was a super strike from Sane, cutting in from the right and curling an unstoppable 25-yard shot past Trapp. Musiala bundled the fifth with the last kick of the match.
It had been 57 days since Julian Nagelsmann's side were last at the summit, but they moved above Union Berlin with a sixth consecutive win on Saturday.
First-half goals from Serge Gnabry, the hugely impressive Musiala and Sadio Mane put them in command at the Allianz Arena, the Senegal forward finishing from the rebound after Robin Zentner saved his penalty.
Silvan Widmer pulled one back on the stroke of half-time just after Sven Ulreich kept out a Jonathan Burkardt spot-kick, but goals from Leon Goretzka and Mathys Tel put Bayern out of sight.
Marcus Ingvartsen capitalised on a terrible mistake from Ulreich to score Mainz's second goal, before the in-form Eric Maxim Choupo-Moting had the final stay with a late goal against his former club.
The champions took the lead in the fifth minute, Mane cutting the ball back and Gnabry finishing with his left foot from close range after a clever dummy from Musiala.
Musiala doubled their lead just before the half-hour mark, finishing off another slick move a clinical-right foot finish after exchanging passes with Choupo-Moting.
Burkardt rattled the crossbar and Jae-Sung Lee struck the post following up before Mane added a third Bayern goal, following up to tuck home after Zentner palmed his tame spot-kick back into his path.
Referee Felix Zwayer awarded that penalty following a VAR check for Alexander Hack's tackle on Mane and he pointed to the spot again after another check on the pitchside monitor, deeming that Ulreich had caught Anthony Caci when attempting to deal with a corner
Ulreich tipped Burkardt's spot-kick over the crossbar, but there was more drama when Widmer nodded in the resulting corner just before the break.
Benjamin Pavard replaced the injured Matthijs de Ligt for a second half that Mainz started brightly, but Choupo-Moting almost restored Bayern's three-goal lead when he hit an upright.
Goretzka duly got on the end of Mane's cross to nod in the Bavarian giants' fourth 58 after minutes and Tel came off the bench to got in on the act with a deflected strike 11 minutes from time.
Ulreich's awful pass gifted Ingvartsen the chance to slot home in the closing stages and there was still time for Choupo-Moting to round off the scoring with his right foot after Kingsley Coman picked him out.
Kane, who scored a hat-trick in their Bundesliga win over Holstein Kiel on Saturday, converted a 19th-minute penalty before goals from Raphael Guerreiro and Michael Olise in the first half on Tuesday.
Bruno Petkovic and Takuya Ogiwara led a fightback early in the second half, with Dinamo hoping to find a way back, but Bayern responded through goals from Kane and Olise.
Kane netted his third and fourth with penalties shortly after, helping him onto 33 strikes in the competition and comfortably past Wayne Rooney's 30-goal record among English players in the Champions League.
Leroy Sane added another in the 85th before fellow substitute Leon Goretzka headed in the hosts' record-breaking ninth finish, the most by one team in a single match since the Champions League was introduced.
Data Debrief: Penalty perfection for Kane
Deadly finisher Kane accumulated 3.76 expected goals (xG) of Bayern's total 6.27 tally for the match, with the 31-year-old finding the target with six of his eight attempts in what proved to be a total domination.
Kane is the first player to score a hat-trick of penalties in a European Cup/Champions League match, and the first Englishman to score four in a match in the competition since Alan Smith for Arsenal against FK Austria Wien in 1991.
There was history elsewhere, however, as Thomas Muller appeared in his 152nd Champions League match for Bayern, breaking Xavi's record for the most matches with one club in the competition (151 for Barcelona).
Vincent Kompany will be looking forward to the rest of this European term, too, after Bayern started a 21st straight campaign in the competition with victory, with their last such defeat coming against Deportivo de La Coruna back in 2002-03.
Muller spent 15 years of an illustrious playing career with Bayern, marking himself as one of the finest goalscorers in the history of the sport.
He remains Bayern's all-time leading goalscorer with 566 in 607 matches and has also netted more times in the Bundesliga (365) than any other player.
Across his time in the German top-flight, Muller won the top-scorer award on seven occasions and five of those were with hauls of at least 30.
His remarkable abilities in front of goal were not just limited to Bayern, however, as he was also Germany's record scorer until 2014 when Miroslav Klose surpassed his haul of 68.
It was as recently as May when Robert Lewandowski broke Muller's record for the most Bundesliga goals scored in a single season, with the man nicknamed 'Der Bomber' amassing 40 in 34 matches as Bayern won the 1971-72 title.
At the end of that season Muller helped West Germany to European Championship success and two years later scored the winning goal to beat the Netherlands in the 1974 World Cup final.
Following his passing, Bayern officials paid tribute to Muller, with the former striker's legacy at the club almost unrivalled by any other individual.
Bayern CEO Oliver Kahn said: "The news of Gerd Muller's death affects us all deeply. He is one of the greatest legends in the history of FC Bayern, his achievements are unmatched to this day and will forever be part of the great history of FC Bayern and all of German football.
"As a player and as a person, Gerd Muller stands like no other for FC Bayern and its development into one of the largest clubs in the world. Gerd will be in our hearts forever."
President Herbert Hainer added: "Today is a sad, black day for FC Bayern and all of its fans. Gerd Muller was the greatest striker there has ever been – and a fine person, a personality in world football.
"We are united in deep sorrow with his wife Uschi and his family. Without Gerd Muller, FC Bayern would not be the club we all love today. His name and the memory of him will live on forever."
The Bundesliga champions and the MLS Cup holders have set up a joint venture named "Red&Gold Football" based in Munich, with the aim of developing players for both teams internationally.
Bayern chief executive Oliver Kahn said the partnership with LAFC will enable Bayern to continue to compete with their European rivals, saying improvements in the quality of MLS will benefit the Bavarian giants.
"On an international level, soccer is developing rapidly, which is also evident in the transfer market," Kahn told the club's website.
"We see this partnership as an opportunity to strengthen FC Bayern in the sporting competition with the best clubs in Europe and the Bundesliga.
"The fact that the 2026 World Cup will largely take place in the United States, where we already have an office in New York, makes Los Angeles even more attractive.
"I expect a boost in quality and young talent in Major League Soccer, which will have a positive impact on our partnership."
LAFC co-president and general manager John Thorrington said: "A partnership of this magnitude is the next step in our evolution as a club. We are extremely excited to work together with FC Bayern to identify and develop young talent in Southern California and beyond.
"We believe this relationship will provide players throughout our systems with the ability to maximise their potential and see a clear pathway to first-team football."
The sides envisage the partnership could grow to include other clubs and development academies across the game in the future "as part of a global development initiative".
Parts of Germany and Belgium were heavily hit by floods over the last fortnight. Over 100 people are still missing, with Germany's official death toll standing at 177, while thousands more have been made homeless.
Two of the worst-hit areas have been North Rhine-Westphalia and Rhineland-Palatinate, while storms have also caused disruption in Bavaria.
In response, Bayern have pledged a minimum aid package of €1.1million, with €1m split between the regions in the west, and €100,000 going towards helping to repair damage in the south.
The Bundesliga champions have also arranged to play a friendly against Schalke, who are based in the North Rhine-Westphalia city of Gelsenkirchen.
Schalke were relegated to the second tier last season, though with the date for the charity game at Veltins Arena not yet confirmed, Bayern pledged the financial support immediately.
"The images of the flood disaster shocked us," said Bayern president Herbert Hainer.
"In such a terrible situation, we have to stick together as a society. Football also lives very much from solidarity and social responsibility. We can only guess what the people in the affected regions have gone through and continue to go through.
"We also want to support them with our charity game and the donation... is on the side of the flood victims.
"I would like to thank FC Schalke 04 very much, Schalke immediately agreed to take part in our initiative. On the occasion of the charity game, together we will also commemorate the people who tragically lost their lives in the storm."
Kompany has joined Bayern on a three-year deal, and comes in as Thomas Tuchel's replacement.
The former Manchester City captain, who began his coaching career in Belgium with Anderlecht, could not keep Burnley in the Premier League in 2023-24.
Indeed, the Clarets were relegated following a 2-1 defeat to Nottingham Forest at Turf Moor in their penultimate match of the season.
Yet, less than two weeks after the campaign's conclusion, Kompany has been installed as boss of one of Europe's biggest clubs.
The 38-year-old joins Bayern after Tuchel confirmed talks over potentially reversing the decision for him and the club to part ways, which came in February, had ended.
Bayern lost their last game of the Bundesliga season to finish in third place, having failed to win any of the four trophies they were in contention for, seeing their dominance of Germany's top tier ended by Xabi Alonso's unbeaten Bayer Leverkusen team.
Alonso had been Bayern's primary target, but their former midfielder has elected to stay at Leverkusen for next season.
Bayern were also linked with Roberto De Zerbi, who has just left Brighton, and Brentford coach Thomas Frank, while they were turned down by Austria coach Ralf Rangnick. Mauricio Pochettino, who left Chelsea on Monday, was also rumoured as a potential option.
Kompany, then, is a surprise pick, but Bayern will be hoping he rediscovers the magic touch he had during his first season at Turf Moor in 2022-23, when he guided the Clarets to promotion from the Championship, earning 101 points in the process.
However, Kompany's possession-based, front-foot approach was badly exposed in the Premier League, with Burnley winning just five games on their way to taking 24 points as they finished 19th, going back down alongside Luton Town and Sheffield United.
He leaves Burnley having managed 96 games, winning 41 (42.7 per cent) of those matches.
In a statement, Burnley said they were "initially confident" of keeping Kompany at the club, but claimed "the changing dynamics of the situation made this impossible".
"We understand the allure and prestige of a club like Bayern Munich and respect Vincent's ambition to explore new opportunities," the statement continued.
"We wish only the best for Vincent and would like to put on record our appreciation for his dedication every single day he was a part of this football club.
"Our priority remains the stability and success of Burnley, and we will continue to take the necessary steps to ensure that our ambition is realised, namely our return to the Premier League."
The 21-year-old has not featured for Bayern since December 17 after testing positive for COVID-19 earlier this month.
Davies had been due to return to action for the German champions this week, but routine medical checks discovered another medical issue.
Bayern boss Julian Nagelsmann confirmed at a news conference previewing Saturday's trip to Cologne that the Canada international will be out of action indefinitely.
"When we did our follow-up examination we do with every player that has had COVID-19, we detected signs of mild myocarditis, an inflammation of the heart muscle," he said.
"He'll sit out training until further notice. He won't be available, also in the coming weeks.
"The ultrasound shows this myocarditis isn't so dramatic, but it's a sign of myocarditis. Still, it has to heal and that will definitely take some time."
Davies has started 22 of Bayern's 27 matches this season – only Manuel Neuer (25), Thomas Muller and Robert Lewandowski (both 26) have started more regularly.
He has made 16 appearances in the Bundesliga this term and leads the way in the division for dribbles attempted (97) and completed (61).
Davies' lay-off is also bad news for Canada as they have two crucial World Cup qualifiers at the end of this month.
While the left-back will sit out Bayern's clash with Cologne, Bayern will welcome back six others from last week's shock 2-1 home loss to Borussia Monchengladbach.
But Nagelsmann will not take any risks when it comes to the fitness of Manuel Neuer, Dayot Upamecano, Omar Richards, Leroy Sane, Corentin Tolisso and Tanguy Nianzou
"None of them are 100 per cent fit," he said. "Some of them had coronavirus symptoms. They're back in the squad, but none except Manu are ready to start or play for long.
Asked about Tolisso's availability, Nagelsmann said: "He had no symptoms and has come back the fittest. We have to see, but he'll be involved."
Leon Goretzka, Kingsley Coman and Lucas Hernandez will miss out this weekend, while Eric Maxim Choupo-Moting and Bouna Sarr are on Africa Cup of Nations duties.
Bayern have won each of their last eight Bundesliga games against Cologne and are unbeaten against them in their last 15 league games (W14 D1).
Steffen Baumgart's sixth-placed side have won their last three league games, however, which is as many as they managed in the previous 14 combined.
Teenager Aleksandar Pavlovic – with his first Bayern goal – and Alphonso Davies put the visitors in command at the interval after Thomas Tuchel’s side had encountered a difficult start.
Harry Kane’s 23rd Bundesliga goal, sandwiched between a Ermedin Demirovic double, eventually proved the difference at a ground where Bayern had lost on their previous two league visits.
Augsburg were left to rue the presence of VAR twice in the opening 12 minutes much to the annoyance of home supporters.
A fifth-minute ball directed towards Demirovic struck the arm of Matthijs de Ligt and a penalty was awarded before a VAR check ruled contact was outside the box.
Augsburg thought they had then taken the lead when Elvis Rexhbecaj drilled past Manuel Neuer from a tight angle, but the midfielder had marginally strayed into an offside position.
Leon Goretzka volleyed wide of a post and Bayern’s improvement produced a 24th minute lead and a moment to remember for 19-year-old Pavlovic.
Raphael Guerreiro corner’s was not properly cleared by Phillip Tietz, and Pavlovic was alert to take a touch before lifting the ball into the roof of the net.
Bayern lost Kingsley Coman to injury and Augsburg had a chance to equalise when Rexhbecaj shot straight at Neuer.
Kane fired wide from a tight angle before Bayern doubled their lead in the fifth minute of stoppage time at the end of the first half.
Goretzka found Davies with a measured pass and the full-back, cutting in from the left flank, drilled home from 25 yards with his weaker right foot.
Augsburg were not finished though and halved the deficit after 52 minutes when Kevin Mbabu sped down the right.
Mbabu delivered an accurate cross for top scorer Demirovic to guide his header beyond Neuer and into the bottom left-hand corner.
Kane restored Bayern’s two-goal cushion six minutes later, rolling home Jamal Musiala’s pass into an empty net.
The offside flag was initially raised, but the goal stood after VAR intervention with the final touch coming off an Augsburg defender.
Bayern almost increased their lead nine minutes from time when Leroy Sane released substitute Mathys Tel and the substitute struck the post.
There was drama to the end as Neuer saved Sven Michel’s penalty and Demirovic converted another spot-kick in the fourth minute of stoppage time, but Bayern held on to make the short trip home with three precious points.
The 20-year-old had missed Bayern’s last two matches with a hamstring issue but returned to training earlier this week.
Germany face Japan and France in international friendlies on Saturday and next Tuesday respectively.
A statement from the club read: “Jamal Musiala will not join up with the Germany national team as planned for their friendly matches against Japan (September 9) and France (September 12) after the Bayern attacking midfielder withdrew from the squad due to a back complaint.”
The news comes a day after Musiala was nominated for the best young player award at this year’s Ballon d’Or ceremony.
The Bayern Munich midfielder’s season-long loan at Ibrox was recently cut short by a hamstring injury and he returned to Germany.
But the United States international was back in Glasgow on Sunday to collect the PFA Scotland Men’s Young Player of the Year award.
The 20-year-old told Sky Sports News: “I hoped for a better ending but it’s quite common in football to get injuries so I am unlucky to be one of them.
“I have had a great time here. It might not be the end – we will see what’s going to happen in the summer.
“It’s 50-50. It’s up to Rangers, up to Bayern and up to me, so it’s completely open.
“I am going to speak to Michael Beale in the coming days and then see what he is saying, see what Bayern are saying, and then I will decide.”
The former Germany Under-21 international beat Celtic pair Liel Abada and Matt O’Riley plus Albion Rovers winger Charlie Reilly to the prize.
“I’m extremely proud and extremely happy,” he said. “In Germany it’s not usual so I am just glad I got voted for. It’s a huge honour. The other nominees deserved it as well.”
The England captain, who did not register a single shot during Saturday's 1-1 draw despite Bayern dominating, was injured in a collision late on at the Allianz Arena, where Aleksandar Pavlovic cancelled out Robert Andrich's earlier effort.
Bayern coach Vincent Kompany was hopeful Kane would be fit to feature against Aston Villa in the Champions League on Wednesday.
On Sunday, Bayern released a statement confirming tests run on Kane had revealed no significant damage, and that the 31-year-old would "continue to receive appropriate treatment", though they did not confirm whether the forward will be fit to face Villa.
Kane suffered the knock due to a robust challenge from Amine Adli.
Speaking to reporters after the match, Kane said: "Sometimes there have been red cards for something like that.
"I'm OK, but it's a bit sore. I think it's OK. It doesn't feel too bad at the moment. We'll assess that in the next few days, but I don't think I'll be out for long."
Villa will certainly be hoping Kane is absent as they prepare to host a European giant.
Kane has been directly involved in seven goals in six career appearances against them at Villa Park, scoring five goals and providing two assists.
Indeed, he has also scored the game-winning goal at Villa Park on two previous occasions, netting a 90th-minute winner in November 2014 (2-1) and both goals in a 2-0 victory there in March 2016 – both during his time at Tottenham.
The Bavarians bounced back from their midweek Champions League loss at Barcelona as they delivered a five-star victory through five different scorers.
It means Bayern have now scored 29 league goals this season, the joint-highest tally after eight games of a Bundesliga campaign. Only they themselves have scored as many goals at this stage of a top-flight campaign, also doing so in 2021-22 and 1976-77.
Kompany ensured his side were in no mood for adventures against Bochum and despite an early chance for the hosts, they dominated the game.
"We played very seriously in this game. We lost here twice in the past three years, so there was no underestimating of the opponent," Kompany told a press conference.
"We conceded a big chance early in the first half, but I liked the fact that we stayed calm."
Bochum's Moritz Broschinski missed that opportunity, seeing his eighth-minute effort cleared on the line, before Bayern scored twice in the first half and another three times after the break.
Bayern are on 20 points, ahead of second-placed RB Leipzig on goal difference. Champions Bayer Leverkusen are in third place on 15. Bochum remain in last place with one point from eight games.
The win also meant Kompany, who had been criticised for Champions League defeats to Aston Villa and Barcelona, became the first coach in Bundesliga history whose team has netted 29 times in his first eight league games in charge.
The Belgian, who succeeded Thomas Tuchel, is in his first season in Munich.
"We stayed calm and serious from the first to the last minute," Kompany said. "The team did a good job. We just want to continue like this.
"We are very happy for what it (victory) does for us in the Bundesliga," he added.
Bayern took a 2-0 advantage into half-time after goals from Harry Kane and Serge Gnabry, but Kevin Sessa and Tim Kleindienst both struck for the hosts early in the second period.
Kleindienst grabbed the winner with 11 minutes to play, putting another dent in Bayern’s already slim Bundesliga title hopes as Thomas Tuchel’s side fell 16 points behind leaders Bayer Leverkusen with six games to go.
The defeat means Bayern head into Tuesday’s Champions League quarter-final first leg with Arsenal on the back of successive defeats.
Bayern had an early effort when Gnabry found Leon Goretzka, who had his shot blocked, and Gnabry was the creator again minutes later, but Thomas Muller – making his 700th competitive appearance for the club – was unable to reach the cross at the back post.
Heidenheim had a chance from a corner but although the delivery was cleared, Kim Min-jae did well to block Jonas Fohrenbach’s shot from the rebound and Muller came close at the other end after pouncing on a loose ball with his eventual shot deflected for a corner.
Bayern took the lead in the 38th minute when Kane latched on to Gnabry’s flicked cross from the right and the England captain tucked the ball into the bottom corner to score his 32nd Bundesliga goal of the season.
They doubled their lead seven minutes later as Alphonso Davies fired in a cross from the left to an unmarked Gnabry in the centre of the box and the Germany winger easily headed the ball past Kevin Muller.
Heidenheim made a triple substitution at the break and the changes immediately paid off when Sessa came off the bench to pull one back in the 50th minute after the midfielder pounced on a loose ball and broke forward to slot home.
They equalised just one minute later through Kleindienst, who got on the end of a deep cross from Jan-Niklas Beste to poke the ball in at the right post.
Bayern tried to restore their lead when Kane’s strike was saved by Muller and substitute Mathys Tel nearly made an instant impact but was also denied by a solid save from the home goalkeeper.
Kane then blasted the ball wide from inside the box.
Heidenheim were also pushing for a winner when Beste picked Sessa out but Sven Ulreich saved his shot and Beste was involved again, curling a free-kick just over the crossbar just minutes later.
Kleindienst then fired the hosts in front in the 79th minute, when Marvin Pieringer teed-up the striker, who rolled the ball into the far bottom corner to seal three points.
Deals worth in excess of €100million have been commonplace in the past four years, with Neymar becoming the world's most expensive player when he joined Paris Saint-Germain for €222m in August 2017.
Bayern have been more conservative but broke their transfer record by splashing out €80m on Lucas Hernandez last year.
Links to Leroy Sane and Timo Werner led to suggestions the Bavarian giants were willing to break the bank again, but Hainer believes the inflation in the market will have been stemmed by the proliferation of COVID-19.
Revenues have dried up for clubs across the world, with players at Bayern, Barcelona, Juventus and Atletico Madrid among those to take pay cuts while football is on hiatus.
Asked about the potential impact of the coronavirus crisis on transfer fees, Hainer told Bayern's 51 magazine: "As I said, although serious predictions are difficult to make, it's obvious there'll be changes. I agree with Uli Hoeness' assumption that transfer fees will decrease. That's just logical.
"When income decreases, there's less money in circulation. And given the economic impact of the coronavirus crisis on people's everyday lives, outrageous sums in the millions are even less justifiable than they already were.
"My hope is that more common sense will be applied here as well. I have to take my hat off to Hasan Salihamidzic and our sporting leadership. They're handling the coronavirus situation very well."
Bayern players agreed to a 20 per cent wage reduction during the Bundesliga suspension, which is scheduled to last until at least April 30.
Hainer acknowledged the situation has put clubs in precarious financial positions, but he is confident Bayern will be able to get through the crisis without "any major damage".
"Of course, the situation is very tense. It's about the existence of individual clubs. And even FC Bayern faces a major financial challenge – that's no secret," said Hainer.
"But our club is in an excellent position. We work day after day to ensure that FC Bayern can navigate through this phase without any major damage.
"Despite this immense task, we're looking to the future with confidence."
Lewandowski returned to full training this week after suffering knee ligament damage while away on international duty with Poland last month.
The striker missed both legs of Bayern's Champions League quarter-final against Paris Saint-Germain as the defending champions were knocked out on away goals, while an extended absence hampered his chances of surpassing Gerd Muller's record tally of 40 league goals, achieved back in the 1971-72 season.
Sitting on 35 with just four games remaining, the 32-year-old is set to make his comeback when Flick's table-topping side visit Mainz on Saturday.
A win on the road will secure a ninth successive league crown and while Lewandowski is also so close to achieving personal glory, the team still comes first for Flick.
"I think we all agree that's his major goal," the Bayern boss told a news conference on Friday.
"He's going to be part of the squad, Leon Goretzka is going to be part of the squad, Serge Gnabry is probably going to be part of the squad. The squad is slowly but surely filling up again – we are returning to normal, which is good of course.
"It's important for us to win the championship - we want to do that as quickly as possible."
On Lewandowski's impending return, he added: "Don't forget that he was out for four weeks.
"He's in very good shape, he showed that in training, but we have to wait and see how he handles the training sessions and the comeback attempt, how his body reacts.
"Of course we will all try to support him, but first of all our focus and priority is the success of the team and the club."
Lewandowski was badly missed as Bayern scored just three goals from 45 shots and eight 'big chances' against PSG. In the 3-2 home defeat in the first leg, the German club's tally of 31 attempts were worth 3.8 expected goals (xG).
Out of Europe, the Bundesliga is the solitary focus for Flick and his squad - but the outgoing head coach expects in-form Mainz to make it difficult to get over the line.
"It's definitely a very deserved championship," he said. "We hope we can win it in Mainz, but we know that they are in really good shape, unbeaten in six games – four wins and two draws – and against some teams who are at the top as well.
"They are a team who are aggressive in defence and very compact. When they win possession, they transition very quickly. These are the things we have to be wary of."
Bayern fought back to record a 5-2 win against Mainz in the reverse fixture, making it the first time since 1988 - and just the fourth occasion overall - that the Bavarians had come back to triumph after being at least two goals down at half-time in the league.