PSG's new star striker had to find the net late to recuse the club from what would have been a shocking loss.
Benoit Pedretti’s fine opening goal had the Corsicans in front before a stunning performance from Guillermo Ochoa in the visiting goal kept the home side at bay. But Cavani scored a beauty from 18 yards to secure a draw just before full time.
However, the Uruguayan's stunning equalizer four minutes from the end ensured Laurent Blanc's side avoided defeat, although this is likely to be scant consolation after statistics showed the club had 39 shots to the visitor's one throughout the match.
It was Cavani's first league start for PSG, while fellow close-season signing Marquinhos was named on the bench by Blanc.
For the visitors, Joshua Nadeau replaced the suspended Benjamin Andre and Sigamary Diarra was preferred to Johan Cavalli.
PSG made the early running, with Zlatan Ibrahimovic's free kick forcing Ochoa into a parried save only for the ball to trickle along the goal line and behind for a corner.
However, Ajaccio went ahead after 10 minutes thanks to a superb effort from Pedretti.
The French playmaker caressed a delicious strike from outside the box into the top corner past a helpless Salvatore Sirigu.
PSG then forced good chances through Ibrahimovic and Maxwell as the club looked to restore parity, but Ochoa was equal to them both.
Sweden international Ibrahimovic again threatened after 33 minutes, chesting a ball down and firing past Ochoa's right post before his knockdown almost forced Ronald Zubar to turn the ball into his own net.
PSG continued to apply pressure but was frustrated for the remainder of the half by a stubborn Ajaccio defense, and went in behind at the break.
The second half began in much the same vein as the first ended, with Blanc's men threatening from the off.
Cavani headed wide two minutes in before Alex forced Pedretti into a goal-line clearance just after the hour mark.
Christophe Jallet scuffed a glorious opportunity wide after 72 minutes as the chances continued to flow for the visibly-frustrated home side.
Ochoa's goal carried on leading a charmed life as Thiago Silva crashed a header against the bar but eventually, the home side was level four minutes from time through Cavani.
The close-season signing from Napoli opened his PSG account in style, turning Zubar on the edge of the area before arrowing a strike into the top corner.
Sensing a winner, PSG continued to push, with the team's captain Silva curling an effort just wide before Ezequiel Lavezzi saw his appeal for a penalty turned away after he went down under the challenge of Laurent Bonnart.
There was still time for a goal line clearance from the home team's defense as well as an excellent Ochoa save from a stooping Marco Verratti header and another shot from Silva that rattled the bar.
However, it somehow remained level, meaning the champion lost further ground to its title rivals after Monaco, Lyon and Marseille all kept up their winning starts to the season over the weekend.