Sandy Baltimore's cross looped in for the opener, but Bayern levelled when Saki Kumagai scrambled in and Klara Buhl's deflected shot put them ahead.

But Bachmann kept her composure in the 112th minute to slot beyond Janina Leitzig at the Parc des Princes.

The French side will face Lyon or Juventus in semi-finals.

A record crowd for a PSG women's game of 27,262 turned out for the quarter-final, but the home side had to battle to get through.

Bayern only named four substitutes because of Covid absentees and suspensions but looked the better side for large spells and were unfortunate to fall behind.

Bayern goalkeeper Leitzig was arguably at fault for the opener, but made amends with a superb save to deny Grace Geyoro and then kept out Kadidiatou Diani.

Kumagai levelled on the night after PSG failed to clear a free-kick, before the German side edged ahead in the 54th minute when Buhl's effort deflected in off team-mate Lea Schuller.

The decisive touch appeared to come off Schuller's elbow, wrong-footing goalkeeper Barbora Votíkova, but the video assistant referee check found no reason to rule it out.

Diani did have the ball in the net for PSG in normal time, but it was disallowed for a foul on Leitzig, who made another smart stop from Marie-Antoinette Katoto moments later.

Bayern tired, though, in extra time and, with PSG able to bring on fresh legs, the hosts capitalised when substitute Bachmann found the far corner with a smart finish with eight minutes to go.