The Argentina winger latched on to a poor clearance by Adama Soumaoro in the final at the Stade de France and rounded goalkeeper Vincent Enyeama to score despite Marko Basa's lunging effort to try and cut out his 74th-minute shot.
PSG, who have already retained the Ligue 1 title, were reduced to 10 men three minutes earlier when midfielder Adrien Rabiot received a second yellow card for a foul on Lille playmaker Soufiane Boufal.
Midfielder Javier Pastore had put PSG ahead with a disputed goal late in the first half, volleying home a punched clearance from Enyeama with Layvin Kursawa in an apparent offside position in the goalkeeper's line of vision.
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Lille, playing in their first final, equalised five minutes into the second period when left back Djibril Sidibe hit a free kick from 22 metres through the wall and past a static Salvatore Sirigu in goal.
(Writing by Rex Gowar; Editing by Tony Jimenez)
