The former Premier League player of the year blasted home from the spot to seal a 5-4 shootout triumph in the Round of 16 after the two sides had finished level at 1-1 after 90 minutes.
After Montpellier skipper Mamadou Sakho and Valentin Rongier had been successful with their spot-kicks, Mihailo Ristic saw his penalty saved by Marseille goalkeeper Pau Lopez, and the visitors couldn't recover and bowed out.
A first half of few chances saw Montpellier largely on the back foot, and the hosts were unfortunate not to go ahead when Payet struck the crossbar from a free-kick shortly before half-time.
The second half followed a similar pattern, and it was no surprise when Marseille did break the deadlock through Arkadiusz Milik, who fired home from inside the box after Montpellier failed to clear the danger.
However, sox minutes later, a speculative ball into the Marseille box found Beni Makouana, and he stretched out a leg to lob the ball over the on-rushing Lopez to level the score and take the match into the shootout.
Lopez atoned for his earlier error as Marseille won the shootout, and pressed on to the last eight.