Second-placed Montpellier were also held 1-1 at Saint-Etienne while Olympique Lyon went down 2-1 at Sochaux with improving Olympique Marseille the only side among the big clubs to register a win with a 2-0 home success over Nice.
PSG took the lead at Bordeaux thanks to Mohamed Sissoko's header on nine minutes but the hosts hit back soon after through in-form Yoan Gouffran after good work by impressive left-back Benoit Tremoulinas.
The game then petered out with 2009 champions Bordeaux, who had been in abject form before a win over Ajaccio last weekend, more than holding their own against the favourites for the title.
Montpellier had similar troubles in breaking down a stout defence after Romanian midfielder Banel Nicolita gave hosts Saint-Etienne a first-half advantage. Joris Marveaux levelled on the hour after a corner.
Fourth-placed Lyon were also playing mid-table opposition in Sochaux but lost despite dominating possession for long spells to slip seven points adrift of PSG after 13 games.
Remi Garde's side went behind to Anthony Reveillere's 10th minute own goal only for Alexandre Lacazette to soon equalise for Lyon with a header.
Inspirational Algerian midfielder Ryad Boudebouz's penalty just before the break after being fouled by Aly Cissokho then handed Sochaux the lead again and the 11th-placed side clung on amid intense pressure.
"If we have to score three goals each time to win, it is going to get complicated," Garde told reporters after Lyon's fourth straight away loss in the league.
"I think the emotional impact of the derbies against St Etienne, the Champions League clash with Real Madrid and lots of matches with almost always the same players means we lacked a bit of freshness."
Olympique Marseille endured a dreadful start to the campaign but shot up to eighth after their third league win in a row, substitute Jordan Ayew heading home on 73 minutes and Loic Remy scoring a penalty in stoppage-time to outwit Nice.
Stade Rennes, whose coach Frederic Antonetti has put his own future in doubt, could only draw 1-1 at home with Valenciennes but went fifth after Toulouse surprisingly lost 2-0 at Auxerre.
Nancy beat Stade Brest 2-1, Caen overcame Dijon 3-0 and Lorient defeated Ajaccio 2-0 in other Sunday matches.
Third-placed champions Lille drew 1-1 with Evian on Saturday.
