Coming into the game, PSG knew that they had something of a mountain to climb, given that Lyon are top of Division 1 Feminine and nine points clear of their rivals.
But PSG were stunningly efficient for so long, gaining a shock 2-0 lead that looked set to take them into the second leg with an advantage.
Lyon spent the first half largely in the ascendancy and had a superb chance just after the half-hour mark, as Constance Picaud in PSG's goal failed to claim a cross, and the rebound dropped to Wendie Renard, but she rushed her finish and could only find the side netting.
And they were swiftly punished, as Marie-Antoinette Katoto got on the end of a delicious delivery from Sandy Baltimore and finished despite being off balance at the back post to give PSG the lead against the run of play.
PSG picked up where they left off in the second half and Katoto added a second just a minute into the half, controlling a deflected shot and finishing coolly to give her side a commanding lead.
But Lyon somehow managed one of the most efficient comebacks fans will ever see.
Kadidiatou Diani first finished a superb run with a poked finish in the 79th minute, then Melchie Dumornay equalised five minutes later with a powerful effort.
And, in the 86th minute, Amel Majri, on as a substitute, finished brilliantly after an exceptional break to give Lyon a scarcely believable victory.