Ten-man Chelsea were forced to put their qualification party on hold after Bordeaux captain Alou Diarra stunned the Blues with an 82nd-minute equaliser.
Nicolas Anelka's 14th goal of the season in the 60th minute should have put Chelsea into the knock-out stages of the Champions League.
But Diarra's headed the hosts level eight minutes from time and Frank Lampard was dismissed for a second yellow card as Chelsea now require a home win against CFR Cluj in their final game to ensure a place in the next round.
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