Neither side could be separated in an entertaining game which finished 2-2 after 90 minutes and saw Montpellier midfielder Marco Estrada shown a straight red card in the second half .
Former Portsmouth midfielder John Utaka opened the scoring for reigning Ligue 1 champions Montpellier when he fired past Hugo Lloris after 27 minutes.
Lyon, last season's Coupe de France winners, equalised after 44 minutes when Bafetimbi Gomis headed home from 12 yards.
Montpellier recovered from that setback after the interval, and regained the lead when debutant Emanuel Herrera struck from the penalty spot after 56 minutes, when Gomis was adjudged to have handled the ball inside the penalty box.
Lyon again restored parity through Jimmy Briand's powerful 77th-minute volley, following good work from Alexandre Lacazette.
Estrada was then sent off two minutes later for a bad lunge on Yassine Benzi.
Although Lacazette missed a glorious chance late on, Lyon still emerged victorious in America when Briand scored the decisive penalty in the shootout.
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