Having faced recent questions over his form and focus, Mbappe responded with a decisive display at Parc des Princes to help Mauricio Pochettino's men to three points.
Mbappe broke the deadlock after Montpellier goalkeeper Jonas Omlin had earlier been sent off for fouling the France star, and he set up Neymar to mark his 100th PSG appearance with the second goal.
Mauro Icardi and Mbappe added two further goals within three minutes as the champions eased to a routine win, their fourth in a row by at least four goals against Michel Der Zakarian's side.
Montpellier, six games without a win in Ligue 1 before this contest, were left with a huge task when Omlin flattened Mbappe following a stunning throughball from Leandro Paredes, with a VAR review leading to the keeper's dismissal.
PSG eventually capitalised on their dominance 34 minutes in, Neymar and Angel Di Maria each playing decisive passes before Mbappe clipped a cool finish over substitute keeper Dimitry Bertaud.
It was Mbappe's 13th league goal of the season and the 13th time he has been assisted by Di Maria in the competition.
Neymar almost doubled the lead before the break but was thwarted by a good save from Bertaud, who then denied Mauro Icardi acrobatically early in the second period.
The second goal came on the hour mark, though, Mbappe teeing up Neymar for a simple finish after a fine lofted pass from Marco Verratti.
With the floodgates suddenly open, PSG scored a further two goals inside three minutes, Icardi drilling high into the net after good work from Alessandro Florenzi and then setting up Mbappe for a routine finish after Neymar led a quick break.
Bertaud did manage to deny Layvin Kurzawa a stunning fifth, tipping the full-back's bicycle kick onto the crossbar.