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The visitors were the first to threaten when Florian Raspentino was allowed to raid to the edge of the box, but his effort crept just past the post.
Jimmy Cabot could have put Troyes ahead as Bastia failed to clear their lines from a cross into the box, but the forward sent his strike wide of the target.
The home side would rue their missed chance as Seko Fofana put the visitors ahead when he latched on to a through-ball from Floyd Ayite and he held his composure to slot his shot past Paul Bernardoni.
Cabot threatened again before the break as he collected the ball from Fabien Camus's cross into the box, but he was unable to hit the target from close range.
In the second half, Troyes drew level as Cabot finally got on the scoresheet as he turned the ball into the top corner after latching on to a loose ball in the box following a corner from Jonathan Pereira.
Yoann Court could have stolen all three points for the home side when he weaved his way into the box and fired at goal, but saw his strike clatter off the post and bounce clear.
There was time late in the game for the visitors to press for the win, although Ayite was unable to beat Bernardoni with his shot as both teams settled for a point apiece.
Bastia move up one place into 17th following the draw, while Troyes remain bottom of the table.