The French international winger scored with only four minutes on the clock, and the hosts dominated the rest of the opening 45 minutes at the Stade Velodrome without adding to the scores.
Ayew was found on the left edge of the box by Lucas Mendes on Marseille's first venture forward, and fired powerfully left-footed through Ajaccio keeper Guillermo Ochoa at his near post.
Andre-Pierre Gignac had a couple of chances to extend their lead but twice wasted good crosses from Dimitri Payet, slicing wide on eight minutes and heading off target just before the half hour.
Payet was more accurate with his own shooting as he tested Ochoa with a 25-yard shot on 32 minutes, and the Mexican stopper also had to save from Ayew and Saber Khelifa in a busy first period.
Ajaccio, who are 15 points adrift of safety with only six games remaining of the season after tonight, have so far failed to register a shot on target against a side that are 14 places above them in the table.