Gregory Pujol opened the scoring from the kickoff when he found the bottom-left corner.
The scores were level 10 minutes later when Filippi turned the ball into his own net.
The central defender made amends on the half-hour mark though, when he headed in from Damjan Djokovic's corner.
© Getty Images
Ajaccio's lead was extended before half time when Djokovic struck into the bottom-right corner from the centre of the penalty area.
Neither team could break through the opposition defence in the second half until the 68th minute, when Wael Larbi's shot from a tight angle hit the side-netting.
Hatem Ben Arfa's shot was saved three minutes later, before the former Newcastle United man struck off target.
Jerome Le Moigne saw red in the 88th minute but Ajaccio were able to hold onto the victory.