Michael Ciani scored at both ends and Bordeaux missed two penalties as the French champions leapfrogged Bayern Munich to move to the top of group A with a 2-1 win while the visitors finished the game with nine men.
Ciani first put Bayern ahead with an own goal in the sixth minute before making amends with a fine equaliser in the 29th minute.
Bayern were reduced to 10 men when they lost Thomas Muller on the half-hour mark and Marc Planus then scored the winner in the 41st minute.
Bordeaux could even afford to miss two penalties with Hans-Jorg Butt saving from both Yoann Gourcuff and Jussie while the visitors ended the game with only nine men as Daniel van Buyten was sent off for committing the foul which led to the second penalty in the 88th minute.
Bayern got off to a dream start when Ciani diverted a Philipp Lahm corner into his own goal after six minutes.
But there was only one team in the game for the rest of the first half with Bordeaux coming close to setting the record straight in the 18th minute when Butt pushed away a Marouane Chamakh free-kick which curled wickedly at the last minute.
Ciani then made amends for his own goal with an almost carbon copy, this time at the right end as he met the ball at the near post with an exquisite backheel just inside the post in the 29th minute.
The home team were assisted in their search for three points when Muller was shown the red card for a second bookable offence.
His foul from behind on Matthieu Chalme may even have been worthy of a straight red, but either way, his dismissal left the Bavarians with just 10 men for an hour.
Bordeaux soon took advantage of their extra man with Gourcuff forcing a fine save out of Butt from 25 yards.
And they went ahead in the 41st minute when Hamit Altintop tried to clear a Wendel free-kick, but he only managed to divert the ball against the foot of Planus and into the top corner.
The game seemed to be over for Bayern, but they showed an excellent fighting spirit with Luca Toni pushing his weight around, despite cutting a lonesome figure in attack.
He and Miroslav Klose both had half chances to bring Bayern level before Butt risked everything by giving away a needless penalty in the 65th minute.
The experienced goalkeeper opted not to clear a backpass and found himself caught in possession outside his goal by Chamakh, who made quite a meal of his fall, but earned a penalty nonetheless.
Yourcuff's cheeky attempt to chip the ball over Butt did not succeed as the Bayern goalkeeper managed to stick out an arm to keep the ball out before Gourcuff placed the rebound wide.
The France international's miss almost proved costly as Toni hit the base of the post at the other end from Mark van Bommel's sweeping cross.
Bayern were reduced to nine men when Van Buyten gave away the second penalty of the night, but Butt made another save, this time from Jussie, with two minutes to go.
Teams:
Bordeaux Carrasso, Chalme, Ciani, Planus, Tremoulinas,Plasil (Gouffran 85), Menegazzo, Diarra, Wendell (Jussie 84),Gourcuff, Chamakh.
Subs Not Used: Rame, Jurietti, Cavenaghi, Bellion, Sane.
Booked: Chamakh, Gourcuff.
Goals: Ciani 29, Planus 41.
Bayern Munich Butt, Altintop, Van Buyten, Badstuber, Lahm,Van Bommel (Ottl 78), Tymoschuk, Schweinsteiger,Klose (Pranjic 74), Muller, Toni (Gomez 77).
Subs Not Used: Rensing, Demichelis, Gorlitz, Sosa.
Sent Off: Muller (30), Van Buyten (88).
Booked: Muller, Badstuber, Tymoschuk.
Goals: Ciani 6 og.
Att: 30,267
Ref: Terje Hauge (Norway).