Lyon named an unchanged side from last week's 2-0 first leg win in Munich, while Bayern manager Alexander Straus decided to shake things up, making five changes for this match.
Bayern pushed forward from the off, pinning the hosts back in their own half as the German side looked for a goal to ignite the tie and the visitors rocked Lyon when Klara Buhl put them ahead 12 minutes before the break.
Buhl played a one-two with Momoko Tanikawa before driving forward into the area and drilling a low shot past keeper Christiane Endler which went in off the far upright, just the second goal Lyon had conceded in this season's competition.
"Honestly it's just not good enough from us," Lyon midfielder Lindsey Heaps said at halftime.
"It's a difficult one, they come in with no pressure on their back and they go for goal. We just need to be better and focused."
Focussed they were, as less than 30 seconds after the interval, Lyon restored their two-goal cushion with Melchie Dumornay heading in from a Kadidiatou Diani cross, and an awful mistake at the back saw Bayern fall further behind in the 54th minute.
Giulia Gwinn lost control of the ball inside her own area and Diani pounced to send her shot into the net and six minutes later Lyon put the tie out of reach when Tabitha Chawinga finished off Diani's cross with a close-range strike.
Last year's finalists threatened to run riot, with Bayern needing keeper Maria Luisa Grohs to keep out efforts from Damaris Egurrola and Selma Bacha, before Ada Hegerberg scored Lyon's fourth goal in added time.
Arsenal advance after battling back from two down
Arsenal's women produced a thrilling fightback from a 2-0 first leg defeat to beat Real Madrid 3-0 on Wednesday and set up a Champions League semi-final with eight-time winners Lyon.
Alessia Russo scored twice for the Gunners in front of a crowd of 22,517 at the Emirates, either side of Mariona Caldentey's header, to fire Arsenal into the last four.
"It still feels a bit surreal right now, I've not really let it sink in yet," said Russo of her best night since a high-profile move from Manchester United in 2023.
"We had a lot of belief all week, we knew what we wanted to do, we knew what we were capable of as a team and we have done that tonight."
Madrid arrived in London full of confidence after beating Barcelona for the first time in a women's Clasico on Sunday.
However, the Spanish giants were made to wait for a first Champions League semi-final by a dominant Arsenal performance.
The home side's pressure bore no fruit before the half-time break and indeed they were thankful to a fine save from Daphne van Domselaar that prevented Filippa Angeldahl from adding to Madrid's aggregate advantage.
Three goals in the first 14 minutes of the second half transformed the tie.
Russo swept home Chloe Kelly's dangerous cross just seconds after the restart.
Kelly then picked out former Barcelona midfielder Caldentey to head in just three minutes later.
Russo produced an acrobatic finish to complete the comeback on the hour mark after Madrid failed to deal with a free-kick into the box.
The England striker thought she had a memorable hat-trick only for VAR to intervene and rule out an Arsenal fourth for offside.
But Renee Slegers' side held out to march into the semi-finals, where the French champions will be waiting.