With the score locked at 2-2 after normal time, the match was decided by the lottery of spot-kicks, with Jimmy Briand scoring the decisive penalty.
Montpellier were reduced to 10 men in the second half when midfielder Marco Estrada was shown a straight red for a lunge on Yassine Benzi.
Montpellier, the reigning French champions, retook the lead through Emanuel Herrera's penalty in the second half but Briand again put Lyon - winners of the Coupe de France - back on level terms on 77 minutes.
Estrada was dismissed two minutes later but Lyon could not capitalise on their man advantage and the match ended all square.
Briand was the Lyon hero in the shoot-out to settle the French season's traditional curtain-raiser.