Thirty plus shots on goal were not enough to give the Parisians three points thanks to the heroics of the visitors' goalkeeper Guillermo Ochoa
Benoit Pedretti’s fine opening goal had the Corsicans in front before a stunning performance from Guillermo Ochoa in the visiting goal kept the hosts at bay. But Cavani scored a beauty from 18 yards to secure a draw just before full-time.
However, the Uruguayan's stunning equaliser ensured Laurent Blanc's side avoided defeat, although this is likely to be scant consolation after statistics showed they had 30 plus shots to the visitors' one throughout the match.
It was Cavani's first league start for the club, 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.
It was PSG who made the early running, with Zlatan Ibrahimovic's free-kick forcing Guillermo 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.
The champions then forced good chances through Ibrahimovic and Maxwell as they 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-hand post before his knockdown almost forced Ronald Zubar to turn the ball into his own net.
PSG continued to apply pressure but they were frustrated for the remainder of the half by a stubborn Ajaccio defence, 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 were 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 their 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 hosts' defence 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 champions lost further ground to their title rivals after Monaco, Lyon and Marseille all kept up their winning starts to the season over the weekend.