PSG collapsed from two goals up to lose at Monaco in its previous league game and again failed to make the most of an advantage after Neymar had turned Sunday's (AEDT) match in its favour.
The champion trailed to debutant Timothee Pembele's 10th-minute own goal, but Neymar equalised with a penalty he won himself for his 50th Ligue 1 strike in his 58th appearance – a 21st-century record – and then had a hand in Moise Kean's swift second.
Thomas Tuchel's side was comfortable until 20-year-old PSG academy graduate Yacine Adli brought Bordeaux back level less than two minutes after his introduction, dealing the capital club another early blow in its title defence.
Second-placed Lille can now move level on points at the summit with victory at Saint-Etienne on Monday (AEDT), perhaps sensing an opportunity as PSG stumbles from one blunder to the next.
Pembele's headed own goal from Hatem Ben Arfa's corner, needlessly conceded by Presnel Kimpembe, set the tone for the chaos that was to come.
Benoit Costil saved well from Alessandro Florenzi following wonderful work by Rafinha, but the goalkeeper was outwitted by Neymar from 12 yards after the Brazil superstar took possession from Ben Arfa, tempted a trip from Otavio and successfully appealed for a VAR (video assistant referee) review.
PSG was in front just 65 seconds later as Costil clumsily spilled Neymar's shot and Kean rifled in the rebound.
Costil was more convincing as he turned Kylian Mbappe's finish over and produced an even better save moments later to help an effort from the same man on to the post, before Sergio Rico got down to a Mehdi Zerkane attempt at the other end.
An exquisite Mbappe backheel was ruled out for offside shortly after the restart and PSG was made to pay when Adli shaped a fine finish inside the right-hand post from Ben Arfa's square ball.
Ben Arfa appeared determined to rock his former side further, sending substitute Nicolas de Preville clear to see a shot saved, but had to settle instead for a point that represents a far better result for his current employer.