PSG are level with Montpellier on 60 points from 29 games but the unfashionable southern side, who reclaimed top spot on Saturday thanks to a last-gasp 1-0 win over St Etienne, lead on goal difference.
Visitors Bordeaux took the lead on 77 minutes when Nicolas Maurice-Belay set up Cheick Diabate who scored into an empty net but Guillaume Horau equalised for the hosts four minutes later with a powerful shot from a superb Mathieu Bodmer heel pass.
Bordeaux moved up to eighth place on 41 points.
Four days after their first defeat in four months in the French Cup, Paris played poorly once again.
"Obviously, it was not a good game. We struggled to develop our moves, we had to react once again," PSG football director Leonardo told French television Canal+.
"This game had been exhausting because we did not have the control. You suffer when you trail your opponent on the scoreboard," he added.
Paris had the first chances but Alex headed the ball against the post on 29 minutes and keeper Cedric Carasso brilliantly denied Mohamed Sissoko shoot from outside the box.
Bordeaux reacted when Jaroslav Plasil hit the woodwork five minutes before Diabate netted. Keeper Salvatore Sirigu had to make a superb save to deny Diabate again only one minute after Hoarau equalised.
Toulouse climbed back to fourth when they defeated bottom side Auxerre 1-0 at home thanks to a Franck Tabanou goal.
Tabanou shot from outside the box on 38 minutes to take his side to 50 points, three adrift of third-placed Lille.
Auxerre, who appointed Jean-Guy Wallemme as their new coach this week, are on 24 points, five from safety.
Koro Kone and Younousse Sankhare scored either side of halftime to help Dijon beat Caen 2-0 at home.
Dijon moved up to 13th on 33 points and Caen stayed 17th, just above the relegation zone on 29 points.