Thauvin struck with two minutes left and Cuisance added another in stoppage time after Arkadiusz Milik's opener for Marseille had been cancelled out by Lilian Brassier, to lift the Provence side up to fifth on 45 points from 29 games.
Three days after claiming their first win in two months in a rescheduled match against Stade Rennes, Marseille were put on the right track by Milik's third goal in six games.
Marseille dominated but lacked sharpness and they were punished in the 71st minute when Brassier headed home from Romain Faivre's cross to score. It was only the visitors' second attempt of the game.
Thauvin, however, restored Marseille's advantage with a powerful left-footed effort before Cuisance put the result beyond doubt two minutes into stoppage time with a beautiful volley.