Mbappe got one himself as PSG showed no signs of missing the injured Neymar or Edinson Cavani on a night when they made their lead at the top of the table look all the more unassailable.
Kurzawa headed the hosts into the lead when he connected with Dani Alves' curling cross from the right, glancing the ball down into the bottom-left corner of Benjamin Lecomte's net.
Di Maria should have doubled the lead when he went one-on-one with Lecomte but fired straight at the goalkeeper's legs and shortly after the visitors were level.
Mollet bent a free-kick from just outside the box towards the top right corner, where Gianluigi Buffon managed to push it away but only after the ball had crossed the line, goal-line technology confirmed.
But the best of the first half was still to come as Di Maria stepped up in stoppage-time to send a blistering free-kick around the wall and in off the underside of the crossbar from all of 30 yards to restore his side's advantage.
Julian Draxler fired just wide from 12 yards at the start of the second half and Lecomte made a superb one-handed save to deny Mbappe at close range.
PSG had two goals disallowed for offside, first when Mbappe finished off a sweeping set-piece and moments later when Eric Maxim Choupo-Moting chipped Lecomte in a one-on-one, with the flag having been raised on both occasions.
The hosts' third goal eventually arrived when Nkunku connected with a corner and his header was diverted past Lecomte by the head of Petar Skuletic, who was attempting to force it wide but succeeded only in finding the net.
Hilton endured a bizarre end to the game as he got the final touch on PSG's fourth and fifth goals, twice getting in the way of shots from Mbappe but on both occasions deceiving Lecomte and ensuring the final score was an emphatic one.
What does it mean? One hand on the trophy
Second-placed Lille would need PSG to lose five games in order to catch them and that looks highly unlikely, even with the injuries in Tuchel's squad. The champions are playing in a manner that would leave even their most ardent rivals hard-pressed to claim they do not deserve to retain the title.
Mbappe leads the line
There was a time when the absence of Neymar and Cavani would have worried PSG's supporters, but the form of Mbappe and Di Maria at the moment means they are never short of creativity and firepower.
Hilton checks out
It was a nightmarish second half for the Montpellier captain, who got a touch on the last two goals but was hapless to do anything to prevent them.
What's next?
PSG will hope to make it four straight Ligue 1 wins when they face Nimes on Saturday, while Montpellier have a tricky home game against Reims.
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