Former West Ham winger Payet broke the deadlock on 55 minutes from the penalty spot after Bouna Sarr was brought down in the area by Vincent Bessat.
Thauvin sealed a fourth straight league win for Marseille with his team-leading 10th goal of the season on 74 minutes, curling a terrific 20-yard strike into the top corner.
Rudi Garcia's team moved two points clear of Lyon, who host runaway leaders Paris Saint-Germain in the game of the weekend on Sunday.
PSG are nine points clear following Wednesday's record-breaking 8-0 rout of Dijon at the Parc des Princes.
Defending champions Monaco, in fourth, are at home to bottom-of-the-table Metz.