Gueye smashed in the opener inside the opening 15 minutes at Parc des Princes as Mauricio Pochettino's side prospered despite the continued absence of Lionel Messi, who was missing for a second consecutive game.
The final margin perhaps flattered Montpellier, which appeared to lack attacking intent despite netting 15 times in its first seven league games, while the hosts carelessly wasted chances through Kylian Mbappe and Neymar.
However, substitute Draxler added a late second as PSG moved 10 points clear at the summit, albeit Marseille does have two games in hand as it aims to make up early ground on the leader.
Gueye spurned the first chance of the contest as he sliced wide from Abdou Diallo's cut-back pass, before Neymar chipped narrowly over and Mbappe was denied by Jonas Omlin's legs in a frantic opening five minutes.
However, the hosts managed to break the deadlock through Gueye, who arrowed a left-footed thunderbolt from the edge of the area into the roof of the net from Angel Di Maria's offload.
Teji Savanier's free-kick almost drew Montpellier level immediately, Keylor Navas parried the attempt away, before Ander Herrera's left-footed volley was denied by the crossbar moments before the break.
Omlin had to react quickly after the interval to push away following Mbappe's deflected pass off Nicolas Cozza, with Navas then stopping Stephy Mavididi's low curler at the other end.
Mbappe should have added two goals within as many minutes, but his hesitation derailed the first chance before rounding the goalkeeper with his second and slicing his shot wide.
PSG continued to struggle to kill the game off, Neymar uncharacteristically poking wide from close range, but Draxler managed to slide through the legs of Omlin to finally secure victory in the 88th minute.