Bordeaux, leading 1-0 from the first leg, went further clear through an early Yoann Gourcuff free-kick and with the visitors down to 10 men from the 60th minute they appeared to have the tie firmly in hand.
Not so. The Greek side levelled through Kostas Mitroglou in the 65th minute and Bordeaux were reeling when captain Alou Diarra was sent off three minutes later.
"We made it hard for ourselves in the second half," Gourcuff told French TV channel Canal Plus. "But we had a fantastic first half, we should actually have been 2-0 or 3-0 up at the break."
"Now, we just hope to avoid Barcelona," coach Laurent Blanc told reporters.
His Olympiakos counterpart, Bozidar Bandovic, said: "Congratulations to Bordeaux. I think we were the better side in the second half. If the players had had more self belief, it could have been a different story."
Blanc's side, who had conceded only two goals from eight games in the competition, could have secured their qualification before the break.
Bordeaux's game deteriorated but the French champions held on until Chamakh sealed their progress when he headed home at the far post from a Tremoulinas cross.
