Mbappe had a first-half penalty saved in his first competitive outing of the campaign after suspension and injury, but he made up for that by converting following a Neymar corner in the second half.
Earlier, Falaye Sacko’s own goal gave PSG a 39th-minute lead at the Parc des Princes, and Neymar netted a spot-kick to make it 2-0 at the break.
Neymar nodded in his second and his side’s third goal six minutes after the break, before Wahbi Khazri pulled one back for Montpellier.
Mbappe got the fourth goal on the night for the reigning French champions, and Neymar thought he had a hat-trick only to be denied by an offside decision.
However, recent signing Renato Sanches came off the bench to score PSG’s fifth, with Enzo Tchato pulling another back for Montpellier at the death.
The Parisians have won all three competitive outings at the start of this campaign, scoring 14 goals already under new coach Christophe Galtier.
Neymar has five goals to his name.