Facundo Medina's foul on Matteo Guendouzi resulted in a penalty which Dimitri Payet stroked into the bottom right corner.
Both sides had their chances to add to the score but it fell to debutant Cedric Bakambu to secure the points for Marseille in the 76th minute, latching on to a through ball from Guendouzi and drilling the ball home.
"I'm happy, we have the three points," Bakambu, who signed from Beijing Guoan last week, told the press.
"We have a good defensive base, we are good with the ball... For an attacker, it's easier to find space and to be decisive."
Marseille are now one point ahead of third-placed Nice and 10 points behind leaders Paris Saint-Germain who host Reims on Sunday. Nice will go back into second if they win at Metz.