Lucas Moura and Adrien Rabiot put the visitors 2-0 in front inside 20 minutes, but proceeded to let in three goals in the most incredible collapse
Lucas Moura and Adrien Rabiot put the Ligue 1 champions two goals in front, but incredibly they proceeded to throw away their advantage.
Ryad Boudebouz pulled a goal back on 32 minutes before Francois Modesto and a Julien Palmieri double completed the most dramatic of comebacks.
PSG looked threatening from the kick-off and were rewarded inside the opening 10 minutes as Lucas broke the deadlock with a composed finish.
Yohan Cabaye played a superb long pass over the top of Bastia's defence and Lucas held off the challenge of Florian Marange before lifting the ball over the onrushing Alphonse Areola.
Lucas should have doubled his tally three minutes later having been released by Zlatan Ibrahimovic, but he dragged his shot wide of Areola's goal.
PSG did not have to wait long for a second goal, though, as Rabiot netted in the 20th minute.
The midfielder was the beneficiary of some assiduous work from Blaise Matuidi and Maxwell, who combined to steal possession and set up Rabiot to fire home first time from 12 yards.
Despite their dominance PSG then gifted the hosts a way back into the game after Van der Wiel handled a right-wing cross, with Boudebouz coolly slotting the spot-kick past Douchez.
And, on the brink of half-time, Bastia were level as three PSG defenders failed to clear a corner, allowing Modesto a free header from close range.
No doubt frustrated at throwing their lead away, PSG came out in full attack mode in the second half, with Ibrahimovic the first to test Areola from a 20-yard free-kick.
However, a stunning volley from Palmieri gave the hosts the lead four minutes before the hour, the 28-year-old firing into the top corner after PSG poorly cleared a left-wing corner.
To add to the hosts' frustrations, they were denied an equaliser after 69 minutes as Silva's half-volley thundered against the crossbar from a right-wing free kick.
Still Blanc's side pushed for a leveller, but it was Bastia who got the final goal as Palmieri met Abdoulaye Keita's cross to volley past Douchez and give the Corsicans a memorable victory.