Montpellier still has not won an away game this season.
Things did not start well for Montpellier, whose striker Djamel Bakar picked up a knee injury in the opening minute and was replaced by Victor Hugo Montano.
The Montpellier defense was quite shaky in the first half as a poor first touch from Vitorino Hilton gave Thauvin his first chance of the match in the 20th but he was denied by goalkeeper Geoffrey Jourdren. A weak backpass from Montpellier winger Morgan Sanson then forced Jourdren to rush off his line and knock the ball away in the 23rd.
Marseille could have reached halftime with a bigger lead but Jourdren parried free kicks from playmaker Mathieu Valbuena in the 34th and striker Andre-Pierre Gignac in the 39th before getting the better of Thauvin in the 42nd.
The hosts had no trouble to protect their lead in a lackluster second half despite a wide effort from Montpellier midfielder Remy Cabella in the 69th. Gignac had a curling shot palmed away by Jourdren in the 71st. In the third minute of stoppage time, Thauvin led a counterattack and found Khalifa, who fired through the legs of Congre to beat Jourdren.
"We're starting to feel the pressure from behind," Montpellier midfielder Benjamin Stambouli said. "We'll have to hang tough."
Montpellier remained in 16th place, five points above the relegation zone.
On Saturday, it's: Monaco vs. Rennes; Guingamp vs. Nantes; Lorient vs. Nice; Saint-Etienne vs. Rennes; Toulouse vs. Sochaux; and Valenciennes vs. Lille.
On Sunday, leader Paris Saint-Germain hosts Lyon, Ajaccio visits Bordeaux and Bastia faces Evian.