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It was Ajaccio who got off to the better start, when poor defending from the hosts led to Lasne picking the ball up on the edge of the box before curling a beautiful shot into the far top corner in the seventh minute.
Lasne nearly doubled the visitor's lead five minutes later but Ali Ahamada made the save after the Ajaccio man tried to squeeze the ball past the goalkeeper.
Serge Aurier had a wonderful opportunity to draw the hosts level in the 17th minute when he was found unmarked at the far post with a cross, but he failed to head at the target.
Toulouse got the leveller they deserved just three minutes before the break when Sylla was picked out at the far post to guide home the equaliser in mid air.
Neither side could find a winner in the second half as Toulouse climb to 14th in Ligue 1, while Ajaccio move a point ahead of basement club Sochaux ahead of Sunday's matches.