After Layvin Kurzawa's opener for the champions was cancelled out by Florent Mollet in some style, Di Maria struck a wonderful curling free-kick that crashed in off the crossbar and set the tone for the rest of the evening at Parc des Princes.
Thomas Tuchel's men were at their free-flowing best and Christopher Nkunku netted a header before Montpellier captain Hilton turned Kylian Mbappe's shot into his own net.
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 host's 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.