Marseille malaise drags on before Inter match
Winger Andre netted a Johan Cavalli cross in the 89th minute.
Marseille, who have not scored a goal during the dreadful run, travel to Inter Milan for their Champions League last-16 return leg on Tuesday having won the first game 1-0.
Didier Deschamps' side stay eighth on 39 points from 27 games, eight points short of the third place and a Champions League qualifying spot. Ajaccio climbed up to 13th with 29 points.
Marseille had banked on forwards Loic Remy and Mathieu Valbuena to revitalise the team after returning from injury.
But both France internationals started on the bench and failed to inspire their team-mates when they came after the interval.
Ajaccio had the best chances in the first half but goalkeeper Steve Mandanda saved Damien Tiberi's powerful shot and brilliantly parried an Eduardo header one minute after.
Marseille barely threatened in the second half until Jordan Ayew volleyed a Brandao cross only to see keeper Guillermo Ochoa deny him the opener in the 85th minute.