The first half proved to be an even contest, with both sides finding the net before the whistle.
Former Chelsea and Juventus striker Mutu broke the deadlock for the visitors in the 15th minute when he turned in a cross from Benjamin Andre.
Ajaccio's lead only lasted seven minutes, though, thanks to Pierre-Emerick Aubameyang, who found the back of the net from inside the penalty area.
However, within five minutes of the restart, the home side had opened up a two-goal advantage.
The hosts continued to dominate proceedings, but it was the away side who scored the next goal of the game when Mutu found the target from the penalty spot in the 75th minute.
Any chance the away side had of claiming something from the game was ended two minutes from time when Aubameyang scored his second goal of the contest.