French champions PSG have never won the continental crown but they were in front after just six minutes on Sunday through Marie-Antoinette Katoto.
Lyon then replied with goals from Wendie Renard, who marked her 100th appearance in the competition with a 23rd-minute penalty, and two from American international Catarina Macario in the 34th and 51st minutes.
Macario has now scored in eight successive matches for club and country.
Poland’s Paulina Dudek reduced the deficit with a 58th-minute penalty to keep the capital city side in the tie ahead of the second leg at the Parc des Princes next Saturday.
“We are satisfied with the victory,” said Lyon coach Sonia Bompastor.
“We deserved to win because we made sure to cause PSG’s mistakes by putting them under pressure.”
PSG had not lost since their 6-1 defeat in the league at Lyon in November but they went into Sunday’s game under a cloud after midfielder Kheira Hamraoui was dropped following a training ground bust-up with teammate Sandy Baltimore.
Despite a poor performance, PSG goalkeeper Barbora Votikova, who had conceded the penalty with a clumsy challenge on Melvine Malard, redeemed herself with a decisive save in the fifth minute of stoppage time to keep out Ada Hegerberg.
In turn, Malard gave PSG their penalty after handling the ball in the area.
“I have a quality squad and we assume everything collectively,” said PSG coach Didier Olle-Nicolle of Votikova whose poor clearance had also led to Macario’s first goal.
A comical mix-up between Votikova and Dudek gifted Macario her second of the game as well.
“Mistakes are part of the game. Our goalkeeper saved us a few times and at 3-2, she saved us at the end of the game.”
In the other semi-final, played Friday, Barcelona crushed Wolfsburg 5-1 before a women’s world record crowd of 91,648 at the Camp Nou.