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.
De Bruyne limped out of Friday night’s 3-0 Premier League win at promoted Burnley with a recurrence of the problem which prompted his early withdrawal from last season’s Champions League final, and City boss Pep Guardiola later revealed the 32-year-old Belgium international would be sidelined for “a few weeks”.
The club is yet to provide an update on the severity of the damage, but the midfielder’s name was conspicuous by its absence from the 22-man squad list for Wednesday night’s game in Athens when it was published on City’s official website on Monday afternoon.
De Bruyne has been one of City’s key performers since his £55million arrival from Wolfsburg in August 2015, and is widely regarded as one of the most accomplished midfielders in world football.
There was no place either for midfielder Bernardo Silva, the only other member of the matchday squad at Burnley who was not included, or central defender Ruben Dias, who was not involved in the opening league fixture under concussion protocols.
Kalvin Phillips and Jack Grealish, who were unused substitutes at Turf Moor, did make it, as did the versatile John Stones, who sat out on Friday evening through injury.
Squad (in number order): Kyle Walker, Kalvin Phillips, John Stones, Nathan Ake, Mateo Kovacic, Erling Haaland, Jack Grealish, Aymeric Laporte, Rodrigo, Stefan Ortega Moreno, Julian Alvarez, Sergio Gomez, Josko Gvardiol, Manuel Akanji, Ederson, Maximo Perrone, Scott Carson, Phil Foden, Oscar Bobb, Cole Palmer, Rico Lewis, James McAtee.
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.
Europa League holders Sevilla led through Lucas Ocampos' penalty in Budapest but were pegged back before half-time through Leon Goretzka's leveller on Thursday.
Sevilla proved obdurate opponents in the second period, though, and substitute Youssef En-Nesyri came close to ending Bayern's 22-game winning run when put through in the 87th minute, only for Neuer to turn his effort behind.
The Germany international made an even better save for the Champions League winners when he flicked a right foot out to divert En-Nesyri's attempt onto the post at the start of extra time, but the Sevilla forward did appear offside.
Bayern substitute Javi Martinez then scored a 104th-minute winner to leave Sevilla midfielder Rakitic lauding the display of Neuer.
"It's disappointing but that's football," the former Barcelona star told Sky Germany.
"We saw tonight how important Neuer is for them. We had two great chances to go ahead but he stopped them. Then we gave away a silly corner and they scored.
"Nevertheless, we can be proud of how we played against the best team in Europe and we feel well prepared for the league season."
Sevilla had been unbeaten since February and certainly performed better than the last LaLiga side that faced Bayern, who thrashed Rakitic's old club Barcelona 8-2 in the Champions League quarter-finals.
Julen Lopetegui's men begin their domestic season on Sunday against newly promoted Cadiz in LaLiga and Sevilla captain Jesus Navas wants them to quickly put this defeat behind them.
"It was a really even game and in the end it was them who were able to score the winner, but we had our chances," he said.
"We had chances and didn't take them. We need to bounce back and carry on."
Joan Jordan thought Sevilla could take heart from the display, though.
"We should be proud," the midfielder claimed. "We played a great game and we could've won. Little details decide these things and it wasn't our day. We fought until the end to win this trophy for Sevilla."
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."
UEFA confirmed spectators would be allowed inside the stadium in Budapest for the clash between the winners of the Champions League and the Europa League, but no more than 30 per cent of seats will be occupied.
The decision has been taken so the governing body can "study precisely the impact of spectators on the UEFA Return to Play protocol" amid the coronavirus pandemic.
UEFA president Aleksander Ceferin said: "While it has been important to show that football can carry on in difficult times, without fans, the game has lost something of its character.
"We hope to use the UEFA Super Cup in Budapest as a pilot that will begin to see the return of fans to our matches.
"We are working closely with the Hungarian federation and its government to implement measures to ensure the health of all those attending and participating in the game.
"We will not take risks with people's safety."
Bayern qualified for the September 24 showpiece with a 1-0 Champions League final win over Paris Saint-Germain, while Sevilla booked their spot with a thrilling 3-2 victory over Inter in the Europa League final.
UEFA's website lists the capacity of the venue as 68,000, meaning around 20,000 fans would be permitted at the top end of the proposed cap.
