Nolan Roux put the home team ahead in the 61st minute but the lead lasted only five minutes before Richard Socrier hit back.
The point was Ajaccio's second from four games on their travels since their summer return to the top flight, as well as Brest's sixth draw in eight matches.
Ajaccio threatened first when Frederic Sammaritano's corner was headed wide by Mehdi Mostefa.
Christian Kinkela's superb 20-yard effort was then bound for the top corner until keeper Steeve Elana dived full length to not only reach the ball but hold it cleanly.
Mario Licka had Brest's first chance after hesitation by defender Jackson Mendy, but he fired over the bar from 20 yards.
Kinkela then teed up Sammaritano five minutes before half-time but the midfielder's effort was also too high.
The quality of finishing improved after the break and, after Licka's corner took a deflection off defender Carl Medjani, Roux headed home from 12 yards to put Brest ahead.
But a defensive error from Tripy Makonda gifted Ajaccio a swift equalizer. Socrier intercepted his misplaced pass but still had plenty to do, chipping cleverly over Elana to level matters.
Brest had the best chance to win the game when Benoit Lesoimier burst into the box and drew a sharp save from keeper Guillermo Ochoa. Romain Poyet pounced on the rebound and looked set to find the net but Mendy blocked his effort behind for a corner and preserved a point for his team.
