The French treble winners had Willian Pacho and Lucas Hernandez sent off in the final stages but managed to oust the German giants in Atlanta.
Bundesliga champions Bayern, who lost Jamal Musiala just before half-time with a horror ankle injury, shared an intense and even battle with the Parisians and had two goals ruled out for offside.
Bayern had won their last four matches straight against PSG, including a 1-0 Champions League victory last November, before Luis Enrique’s side hit their peak.
“I think we showed our character with two less players, we showed our personality, and we are strong also like that,” PSG’s Achraf Hakimi told reporters.
“We showed that we want to be continue in this competition and go forward.”
Players and nearly 67,000 spectators observed a minute of silence in honour of Liverpool forward Diogo Jota and his brother Andre Silva, who tragically died in a car crash on Thursday.
It was an emotional moment, especially for a PSG side with five Portuguese players in the squad, including starters Vitinha, Joao Neves and Nuno Mendes.
Luis Enrique began with leading Ballon d’Or candidate Dembele on the bench, as he continues his comeback from a quadriceps injury, but Bayern playmaker Musiala was fit to start.
It was FIFA’s expanded tournament’s biggest heavyweight clash thus far and Bayern coach Vincent Kompany said on the eve of the game he would pay to watch a match he described as a “perfect storm”, because of the teams’ similar high-pressing, attacking styles.
The air-conditioned Mercedes-Benz Stadium also produced the perfect conditions for a pulsating game, lit up by supremely talented dribblers on both sides, as well as two elite goalkeepers in Gianluigi Donnarumma and Manuel Neuer.
Khvicha Kvaratskhelia hit the side netting after a razor-sharp PSG counter and forced Neuer into an excelent save, while Donnarumma saved twice from Olise.
Dayot Upamecano headed home from Olise’s free-kick in first-half stoppage time but the defender had strayed offside and it was disallowed, while England captain Harry Kane sent a header off-target when well placed.
– Musiala horror injury –
Unfortunately Musiala suffered a gruesome ankle injury before half-time as he fell following a collision with Donnarumma, with the goalkeeper appearing distraught in the aftermath.
Bayern’s 39-year-old stopper Neuer produced a sensational save to deny Barcola early in the second half as PSG threatened.
With 20 minutes remaining, Luis Enrique sent on Dembele to make the difference and avoid extra-time.
Dembele came inches from doing just that when Neuer gave the ball away outside his area and the Frenchman lunged to try and roll into the empty net, but it trickled just wide of the post.
Eventually 20-year-old Doue found the breakthrough as Kane gave the ball away and PSG attacked in numbers.
Doue, who burst into the limelight in PSG’s run to Champions League glory, fashioned some space on the edge of the box and flashed a low strike home at the near post.
Bayern were given hope as they hunted for an equaliser when PSG defender Pacho was sent off for a high tackle on Leon Goretzka after 83 minutes.
Kane headed home from an offside position before PSG substitute Hernandez was dismissed for an elbow.
Despite their numerical disadvantage Dembele hit the crossbar before sealing their victory after Achraf Hakimi’s run through, and the Frenchman paid tribute to Jota by copying his video-gaming celebration.
“It was very difficult to hear the news,” Marquinhos told DAZN.
“We have got Portuguese players in the dressing room and they were with him only a few weeks ago playing in the Nations League… we wanted to cheer them up.”
Bayern coach Kompany said he was proud of his team’s performance despite their elimination.
“It could have been 2-0 to us, but it didn’t go our way,” said Kompany.
“In the first half we showed them who we are and they had problems with us,” said Bayern substitute Thomas Mueller, who played his last game for the club.
PSG will face Real Madrid or Borussia Dortmund in the semi-finals on Wednesday at the MetLife Stadium in New Jersey. (AFP)