Lyon, eliminated from all European competition in a 2-1 home Champions league defeat by Gent on Tuesday, remain 13 points adrift of PSG, who host Troyes on Saturday.
Lyonn are stuck on 25 points from 15 games with Montpellier up one place to 13th with 18 points.
Hubert Fournier's Lyon got off to a horrid start and never recovered as Montpellier, with Casimir Ninga scoring twice, ripped through their defence on a night to forget for the hosts.
Montpellier went ahead after just eight minutes when Lyon's Maxime Gonalons deflected Jerome Roussillon's cross into his own net at the near post.
Three minutes later, Ninga outpaced Rafael, after collecting a through ball from William Remy, before beating goalkeeper Anthony Lopes from close range to double the hosts' tally.
Lyon responded in the 14th minute. Gonalons's header was parried by stopper Laurent Pionnier, but Alexandre Lacazette had followed the ball in and headed home to half the deficit.
However, Ninga made it 3-1 three minutes into the second half from close range after Roussillon intercepted a poor pass from Rafael aimed for keeper Lopes.
Second-half substitute Souleymane Camara wrapped up the win for the visitors 10 minutes from time after Ryad Boudebouz, having dribbled past a sorry Rafael, set up the striker to score the fourth goal at a stunned Gerland stadium.
Rachid Ghezzal grabed a consolation for the hosts with a curled strike from outside the box in the 84th before Lyon were booed by the home fans after another mediocre performance.
(Reporting by Julien Pretot; Editing by Ken Ferris)
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