The reigning champions 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 were 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 their title defence.
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 review.
PSG were 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 onto 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 were 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 employers.
What does it mean? Testing results limiting rest
With work to do in the Champions League, PSG would presumably like to be able to give Neymar and Co some time off in the league. However, underwhelming results like this might soon find Tuchel's men in a title race.
Ahead of Wednesday's vital European meeting with Manchester United, the champions had to leave both Neymar and Mbappe on for the full 90 minutes here. Each recently back from injuries, it is far from ideal.
Neymar's night until leveller
Prior to Adli's equaliser, it appeared Neymar - whose side warmed up in shirts paying tribute to the late Diego Maradona - would own this game after a clinical spell midway through the first half.
In reaching a half-century of goals in 58 Ligue 1 matches, he achieved the feat in one game fewer than former PSG great Zlatan Ibrahimovic, previously the holder of the best such record since 2000.
It was the first of five Neymar shots, three of those on target, but Bordeaux refused to be beaten.
50 - Neymar has become the fastest Paris’ player to reach the 50 goals milestone in Ligue 1, in his 58th game. In the last 70 seasons, only Andersson (53) and Skoblar (54) have reached this milestone faster in the top-flight. Samba. #PSGFCGB pic.twitter.com/vdegLTp2s4— OptaJean (@OptaJean) November 28, 2020
Mixed bag for old boy Ben Arfa
Ben Arfa scored his first Bordeaux goal against former club Rennes last week and relished the opportunity to hurt more ex-team-mates in the capital.
The mercurial playmaker started brightly, seeing an early shot deflected wide before having a hand in the opener, but his loose touch led to the leveller.
Although that was one of 20 occasions on which Ben Arfa lost possession, he recovered well to create a game-high five chances - including Adli's strike - and completed six dribbles.
Again PSG must bounce back in Europe, visiting Old Trafford in midweek. Bordeaux have eight days before their next league match against Brest.