The midfield general in the mighty Bayern machine won the ball in the centre circle and bundled in after exchanging passes with Robert Lewandowski for the 82nd-minute clincher.
Corentin Tolisso and Thomas Muller had earlier put Bayern 2-0 in front, but Julian Brandt and Erling Haaland brought Dortmund back to level terms.
Victory meant Bayern, whose 32-game unbeaten run ended with defeat at the weekend to Hoffenheim, delivered more success in the Hansi Flick era.
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."
