Marseille put the hosts under pressure in the first half. Gignac struck the woodwork with a cross-shot from the left flank in the 10th before cutting inside in the 21st to curl a shot that bounced off the post.
Marseille capitalized on a turnover from Ajaccio to take the lead. Thauvin won the ball on the right flank and found Payet, whose first-time effort from 15 yards beat goalkeeper Guillermo Ochoa.
Four minutes later, however, Ajaccio converted its first scoring chance to equalize. Perozo connected with a free kick from Cavalli to head in.
Ochoa saved a long-range strike from Payet in the 34th but was helpless when Gignac chested down a cross from fullback Kassim Abdallah to score his sixth goal this season.
Marseille added a third goal in the second half when Payet charged down the left wing to feed Thauvin, who flicked home from eight yards.
The 2010 champions had no trouble to protect their lead despite an effort from Cavalli in the 55th from a tight angle and a long-range attempt from substitute Claude Goncalves in the 78th.
On Saturday, it's: Reims vs. Paris Saint-Germain; Evian vs. Lorient; Lyon vs. Valenciennes; Montpellier vs. Guingamp; Rennes vs. Bordeaux; and Sochaux vs. Bastia.
On Sunday, Lille hosts Toulouse, Monaco visits Nantes, and Saint-Etienne faces Nice.
