Lucas Moura and Adrien Rabiot gave the champions a comfortable lead with two goals in the first 20 minutes.
PSG then threw away their advantage with a Julian Palmieri double, featuring a wonderous volleyed goal, inspiring the most unlikely win for Bastia who started the day second from bottom.
It was a huge missed opportunity for PSG. They could have gone level on 41 points with Marseille who opened the door for their fiercest rivals by losing 2-1 at Montpellier on Friday.
PSG remained third and an opportunity now knocks instead for Olympique Lyon who can go clear at the summit with 42 points if they beat Toulouse on Sunday.
Ryad Boudebouz began Bastia's thrilling comeback with a 32nd-minute penalty after Gregory van der Wiel handled a cross.
Francois Modesto equalised on the stroke of halftime after slack defending allowed him a free header.
Palmieri's heroics began after the break, the 28-year-old smashing a remarkable effort from 30 yards into the top corner in the 56th minute before sealing victory with a last-minute goal and lifting Bastia out of the bottom three.
Before the match began a minute's silence was held for the victims of the deadly attacks in France over the last three days, a solemn commemoration that was followed at all Ligue 1 and Ligue 2 games this weekend.
(Reporting by Ian Chadband, editing by Tony Jimenez)
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