PSG had lost on two of its previous three league trips to Stade de la Mosson, drawing the other, and looked set for another difficult outing after a poor first half that saw it lose two starters to injury prior to Leandro Paredes's own goal.
Montpellier beat PSG in April with a late turnaround but this time it was the visitor's turn to turn the tables in dramatic fashion.
Neymar won a set-piece that saw Pedro Mendes sent off and then sent the resulting 25-yard free-kick into the top-right corner with 16 minutes remaining.
Two minutes later, he set up Kylian Mbappe to finish impressively shortly before Mauro Icardi wrapped up the points to move PSG eight points clear of Marseille at the top.
There was an ugly end to the game, though, as PSG goalkeeper Keylor Navas appeared to be hit by a bottle thrown from a section of the home supporters.