Kylian Mbappe and debutant Renato Sanches were also on target for PSG, who were set on their way following an own goal by Montpellier defender Falaye Sacko as the home side made it two wins from two at the start of their title defence.
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Sacko tried to clear a Mbappe cross but only succeeded in steering the ball into his own net, before his night got worse when he conceded another penalty after handling the ball in the box.
Neymar stepped up for PSG and made no mistake with the spot-kick to give the Parisians a 2-0 halftime lead.
It looked like it was game over when Neymar added a second soon after the break, heading home a rebound as he reacted quickest to the loose ball.
Montpellier were given hope when Khazri pulled a goal back just before the hour-mark, but when Mbappe finally got on the scoresheet 10 minutes later, that was the end of the contest.
Neymar was denied his hat-trick when he had an effort disallowed for offside, but PSG extended their advantage through Sanches on his debut following his move from Lille.
Enzo Tchato pulled another goal back for Montpellier with virtually the last kick of the game, but it was a comfortable victory for the home side.
Earlier, Monaco came from behind to claim a point in a 1-1 home draw with Stade Rennais, a match in which they were reduced to 10 men early and missed a penalty.
Youssouf Fofana was shown a straight red card inside 15 minutes for a stamp on Rennes' Martin Terrier, but Monaco won a first half spot-kick that was missed by Axel Disasi as Rennes goalkeeper Steve Mandanda made the save.
Gaetan Laborde opened the scoring for Rennes early in the second period, but a disastrous error from replacement goalkeeper Dogan Alemdar, on for Mandanda at halftime and who dallied on the ball to allow Breel Embolo to nick it from him and score his first Monaco goal, saw the points shared.