The away side got off to the better start and went ahead in the 17th minute when Souare powerfully headed home from Marvin Martin's corner.
Lille should have doubled their lead eight minutes later, but Nolan Roux could only shoot wide of the near post following Kalou's through-ball.
Roux squandered another chance three minutes before the break after Florent Balmont's cross from the left resulted in the striker heading over from six yards out.
Lille did manage to find a second just short of the hour mark when Gueye slotted into the bottom right corner from the centre of the box.
The home side then wrapped up the win in the 71st minute when Kalou was first to react from a Guillermo Ochoa save to head home.
Lille stay fourth in the table, while Ajaccio slip to 17th.