Efe Ambrose's Celtic shock Spartak
Ambrose in Celtic action
Celtic have now moved to the top of their group having recorded four points from two matches in a section that also has Barcelona and Benfica.
Spartak are pointless.
Nigeria international striker Emmanuel Emenike thought he had helped Spartak to a home win against the Scottish champions with two goals in the 41st and 48th minutes only for the Glasgow club to stage a remarkable fight back.
Emenike brought the game to parity when he equalised in the 41st minute, when he was set by his strike partner Ari to take the game to 1-1.
He gave his team a 2-1 lead in the 48th minute, but Spartak defender Dmitri Kombarov turned in James Forest effort for Celtic equaliser in the 71st minute.
Greek international Georgios Samaras then silenced Spartak fans with his stoppage time winner for Celtic, who paraded Efe Ambrose from start to finish on his Champions League debut.
Spartak finished the game with one man less after Juan Manuel Insaurralde was red carded in the 63rd minute.