Romaric then headed home the decisive goal in the second half after Julian Palmieri had been sent off with the game goalless.
The action intensified after a fairly even 38 minutes when Palmieri was shown a straight red card for Bastia after a dangerous high-footed challenge.
Despite their disadvantage, the home side took the lead five minutes later when Keseru was played in down the right of the box before firing into the back of the net.
However, the visitors equalised in the 58th minute when Serge Aurier raced down the right of the area before brilliantly crossing for Braithwaite to finish.
Bastia went back in front just nine minutes later when Florian Raspentino whipped in a cross to the far post following a short corner for Romaric to head the ball home.
Toulouse almost found a leveller in the dying minutes but Clement Chantome's fierce shot flew past the post.