Hansi Flick's treble-winning outfit struggled against a stubborn Sevilla side who had been unbeaten since February – a run that included a record sixth triumph in the Europa League, formerly the UEFA Cup – and the LaLiga side went ahead through Lucas Ocampos' penalty.
Leon Goretzka levelled before half-time but Bayern's run of 22 successive victories would have come to an end had Youssef En-Nesyri not been thwarted by Manuel Neuer in the dying stages of normal time.
But it was fellow substitute Martinez, linked with a return to Athletic Bilbao after eight years in Bavaria, who scored his first goal since April 2019 to earn Bayern yet more silverware.
Bayern opened their 2020-21 season with an 8-0 rout of Schalke but it was Sevilla who struck first through Ocampos' penalty.
Luuk de Jong's cushioned header reached Ivan Rakitic, and the midfielder – back at the club after re-joining from Barcelona – was barged over by David Alaba, with Ocampos outfoxing Neuer from a no-look spot-kick.
Robert Lewandowski failed to beat Yassine Bounou from a one-on-one as Bayern responded, but he made up for that before half-time, laying the ball back for Goretzka to pick his spot and score the equaliser.
The Champions League winners thought they had the lead within six minutes of the restart after Muller teed up Lewandowski, having initially been presented with the chance himself by the Pole, but VAR spotted Bayern's number nine was offside when first collecting Leroy Sane's pass.
It was one-way traffic thereafter as Bounou denied Serge Gnabry and Diego Carlos blocked the rebound from Sane, who had a goal disallowed himself after Lewandowski was adjudged to have fouled Sergio Escudero in the build-up.
But it was Sevilla who should have won the game in normal time when Jesus Navas released En-Nesyri on a counter-attack, only for Neuer to make the save from an attempt that was too easy to anticipate.
Sevilla had renewed optimism at the start of the additional period, though En-Nesyri looked offside when he aimed an effort at goal that Neuer's right foot diverted onto a post.
And Martinez made him pay five minutes after coming on when he directed a header past Bounou after the goalkeeper could only push Alaba's effort back in front of him.
Leagues across much of Europe have resumed or are on the point of doing so after a long suspension caused by the pandemic.
Players have for the large part been hunkered down at home since March, unable to take part in full training sessions until recent weeks and missing the routine of matches.
That concerns Spanish midfielder Martinez, who believes footballers have become increasingly vulnerable to getting hurt.
Barcelona captain Lionel Messi and Milan striker Zlatan Ibrahimovic are among the big-name players who have suffered recent injury setbacks.
"I am a player who needs match rhythm. The dynamics of playing every few days is not ideal. We don't have a run of training sessions to reach peak form," Martinez told Marca.
"It's easier now to get injuries because we've stopped for longer than ever before and we haven't had a normal pre-season.
"I'm doing quite well and if the coach wants me I believe I'll be ready.
"And the hot weather's coming. Tell me how you can play in Seville on July 6 or 7."
That aspect will not directly affect Martinez but shows his sympathy for the LaLiga stars who could face difficult playing conditions during the Spanish summer.
Martinez is poised to win another Bundesliga title with Bayern, with his arrival in 2012 from Athletic Bilbao having coincided with the start of a period of startling dominance.
An eighth straight title is almost within Bayern's grasp, given their seven-point lead over Borussia Dortmund with five games to go, but Martinez is struggling to enjoy putting the finishing touches to a successful campaign behind closed doors.
And when Bayern went to Dortmund for a crucial game in the Bundesliga last week, Martinez was taken aback by the near-total absence of anyone in and around the stadium.
That is the necessity given concerns about the spread of COVID-19, but Martinez said: "I don't like it. I am very passionate. I need to be yelled at, even if it's to tell me everything. To go to the pitches of Betis or the Bernabeu and have a thousand people telling you about everything. That motivates me.
"My soul fell to my feet when I arrived at Dortmund and saw five people there with their bikes. But I understand that it was necessary to continue."
The 31-year-old midfielder joined Bayern from Athletic Bilbao in 2012 and has won 19 trophies during his time at the Allianz Arena.
However, Martinez has been restricted to just 10 starts in all competitions in 2019-20 and recently entered the final 12 months of his contract.
Rummenigge has opened the door for the Spaniard to move on during the close season, with teams in France and former club Athletic rumoured to be interested.
"We know that he would like to leave the club with a suitable offer," Rummenigge told AZ.
"We wouldn't put any obstacles in his way because he was always a good player and a reliable, serious person. We will always try to find a solution that suits the player."
Rummenigge also reiterated on Wednesday that fellow midfielder Thiago Alcantara, strongly linked with Liverpool, will only be allowed to leave if his valuation is met.
Bayern are also in talks with versatile defender David Alaba over a new contract, while loanee Philippe Coutinho will return to Barcelona later this month.
Martinez headed the decisive goal in Thursday's Super Cup final, securing a 2-1 victory after extra time following first-half goals from Leon Goretzka and Sevilla's Lucas Ocampos.
It was the second time the midfielder has come up with a crucial goal as a substitute in this fixture, having also scored in the 121st minute against Chelsea in 2013 as Bayern reached a penalty shoot-out and won the title.
The familiar circumstances were not lost on Muller or Martinez, who had been on the pitch just shy of five minutes.
Muller told UEFA.com: "We're delighted, it's unbelievable. We're so tired after 120 minutes against Sevilla, a tough opponent.
"We fought hard and showed as a team that we have that winner's mentality, even when we're not at our best.
"Congratulations to the team and to Javi Martínez, our Mr Super Cup."
Martinez made just 24 appearances for Bayern last season without scoring but told Sky Sport: "I always want to give 100 per cent for Bayern and I showed that today.
"Even if I only play 10 or 15 minutes, I try to help the team and I did that today with my goal.
"I'm really happy to win this trophy for a second time. I also scored in 2013, so it's a great night."
The result means it is now 23 wins in a row for Bayern, who have gone 32 games without defeat.
Martinez came off the bench in extra time of Thursday's Super Cup against Sevilla in Budapest and five minutes later he headed in the winner in a 2-1 victory that earned Flick's treble-winning side yet more silverware.
It was Martinez's first goal since April 2019 and it may be the last of his eight-year Bayern career as rumours of a return to LaLiga outfit Athletic persist.
The 32-year-old is in the final year of his Bayern deal, and reports suggest the Bundesliga and Champions League holders want a transfer fee for the midfielder despite Athletic's wish to bring him back to Spain on a free transfer.
"Javi scored the goal and won us the game. Sometimes football writes these stories – this is a beautiful one," head coach Flick told Sky.
"On Wednesday there were reports that he was in Bilbao, yet tonight he scored the winning goal."
Martinez also came off the bench to score an extra-time goal in Bayern's previous Super Cup triumph seven years earlier, when they beat Chelsea on penalties.
This time they triumphed inside 120 minutes, having fallen behind to Lucas Ocampos' penalty before Leon Goretzka levelled prior to half-time.
It may not have been as comprehensive as their season-opening 8-0 win over Schalke in the Bundesliga last week, but Flick was nevertheless pleased with his team's staying power.
"It took the first 15 minutes for us to get into the game," Flick said.
"It was great for me to see the team try to pull through with their mentality – and succeed. In the end, my players went through the pain barrier to win."
