Chelsea suffered a torrid night and slipped to second in Champions League Group A as they were held by Bordeaux and had Frank Lampard sent off.
Petr Cech made excellent early saves from Fernando, Mathieu Chalme and Yoann Gourcuff as Chelsea struggled.
The visitors continued to misfire until Lampard put Nicolas Anelka clean through to score with a low finish.
An unmarked Alou Diarra headed in from a corner to equalise before Lampard was dismissed for two bookable offences.
With Roma's victory over Cluj, the Italians moved a point clear of Chelsea, who must now beat Cluj in their final group match to be sure of reaching the knockout stages.
It is a scenario that Chelsea boss Luiz Felipe Scolari would not have envisaged before the match, but one which looked increasingly likely as the evening wore on.
With Deco suspended, Chelsea brought Michael Ballack into the starting line-up - their only change from the weekend.
And it was soon clear that the visitors would miss Deco's creativity as they struggled to get any kind of foothold on the game.
By contrast, Bordeaux's start to the match was far from sluggish and they tested Chelsea keeper Cech with a range of efforts.
Cech had to be at full stretch to turn Fernando's drive around the post.
The Czech stopper also had to be alert to beat away a stinging effort from Chalme and another from Gourcuff as Chelsea gave their hosts too much time and space.
We played very poor and we made some of Bordeaux's players better than they really are
Chelsea managed only to trouble the referee, who booked John Terry, Lampard and Ashley Cole in the first half.
Those cautions seemed at odds with Chelsea's attitude as they actually looked far from being up for the fight.
Long balls up to an isolated Anelka brought no joy, and Ballack looked short of fitness in a midfield that was misfiring.
Bordeaux must have sensed there was an opportunity for them to beat an English team for the first time and put themselves in a strong position to qualify from the group.
Yet for all Chelsea's lack of urgency up front they remained solid at the back and the hosts could not penetrate to create any real chances.
Instead it was Chelsea who took the lead - from out of nothing - when Lampard split the defence and Anelka raced through, dummied his shot twice and then slid in a low shot.
That proved to be the last contribution from Anelka as he was substituted and Didier Drogba came on to assume the lone striker role.
As the game went through a lull, with neither side looking dangerous, it seemed Chelsea would get away with a below-par display and nick the win that would see them progress.
But they left Diarra completely free at a corner and he made no mistake with his header, directing it in off the near post.
Worse was to come for Chelsea as Lampard was given his marching orders for a clumsy challenge on Fernando.
Bordeaux: Valverde, Chalme, Planus, Diawara, Jurietti, Menegazzo, Diarra, Gourcuff, Gouffran (Cavenaghi 67), Wendell (Obertan 75), Chamakh.
Subs Not Used: Olimpa, Bellion, Placente, Traore, Tremoulinas.
Booked: Gourcuff, Jurietti, Chamakh.
Goals: Diarra 83.
Chelsea: Cech, Bosingwa, Ivanovic, Terry, Ashley Cole, Mikel, Joe Cole (Ferreira 85), Ballack, Lampard, Malouda, Anelka (Drogba 63).
Subs Not Used: Cudicini, Bridge, Kalou, Alex, Stoch.
Sent Off: Lampard (86).
Booked: Terry, Lampard, Ashley Cole, Joe Cole.
Goals: Anelka 60.
Ref: Frank De Bleeckere (Belgium).