France international Mbappe, making his first start of the season, missed a penalty in the 23rd minute, but created the first goal soon after when his low cross was turned into his own net by Falaye Sacko.
Neymar then scored twice – the first from the penalty spot – before Mbappe opened his account for the season with a smart finish at the back post after 69 minutes.
Mbappe looked unhappy throughout the game and refused to celebrate his goal, much to the frustration of a number of his team-mates. He also left a huddle during a drinks break, preferring to wander on his own in the middle of the pitch while his team discussed tactis with coach Galtier.
Mbappe also reacted furiously to Vitinha's decision to pass to Lionel Messi rather than him late in the first half, throwing his arms up in disgust and seemingly refusing to continue with the attack.
Galtier, though, does not believe too much should be read into it and says Mbappe is simply frustrated at being behind his team-mates in the fitness stakes.
"Kylian played his last game three weeks ago so I knew it was going to be tough on a physical level for him," the PSG boss said.
"He's a competitor. He wants to be good and he wants to be good quickly, but a top footballer is not on and off like that; it takes a little time to regain 100 per cent of his athletic abilities.
"When he's at 100 per cent, he'll make the difference even more. These are players who like to score, who want to score, who attack.
"It's a bit normal for him to be disappointed at being a little short physically compared to his team-mates."
Mbappe's penalty miss was just his second in Ligue 1, with both of them coming at Parc des Princes.
PSG midfielder Marco Verratti attributed his team-mate's attitude to that miss and says he does not mind him sulking as it shows he cares about the club.
"Kylian is a player who always wants to do well," the Italy international said. "I think that with the missed penalty he was sulking a bit but that's normal. He's a big player, he always wants to make a difference.
"When he misses something, he's disappointed, that's normal. But afterwards he bounced back with the first goal on which he was decisive, then afterwards with his goal.
"It's good when he is angry because it means that he cares a lot about this team, that he wants to do well, that he wants to make a difference."
Debutant Renato Sanches added a fifth for PSG late in the game, while Wahbi Khazri and Enzo Tchato Mbiayi were on target for Montpellier.
After a 5-0 win over Clermont last weekend, PSG became the first side to score five or more goals in its first two games of a Ligue 1 season since Reims in 1961-1962.
PSG is next in action a week on Monday (AEST) when it visits Lille, the club Galtier guided to the Ligue 1 title in 2020-2021.