The hosts took the lead in the 20th minute when Wissam Ben Yedder found the target from the centre of the box with his left foot.
The visitors pulled level just three minutes into the second half as Salomon Kalou turned in Payet's cross.
However, Toulouse were back ahead in the 56th minute when Braaten collected Ben Yedder's through-ball before finding the target from close range.
Eden Ben Basat made it 4-0 to the home team in the 89th minute when he slotted in from the centre of the box after receiving Braaten's pass.
That was the final goal of the evening at Stadium Municipal, as Lille's hopes of a top-three finish in Ligue 1 this season suffered another blow.