Celtic started on a positive note and stunned their hosts by taking an early lead in the 12th minute after Gary Hooper converted Mikael Ludwig cross.
However Emenike led Spartak's fightback and responded with a goal in the 41st minute to pull the hosts level going into the break, and scored another just three minutes into the resumption of the second half after neat work from Ari da silva to put the hosts in the lead for the first time in the game.
Misfortune befell Spartak in the 71st minute as Dmitiri Kombarov scored an own goal as the home side's defence failed to properly deal with a cornerkick, to hand the visitors a lifeline.
With the scores still 2-2 it seemed like the game was heading for a draw until Georgios Samaras tucked in Emilio Izaguirre's cross in the 90th minute to hand visiting Celtic a stunning away win.
Ambrose Efe played from start to finish and put up a decent display in the game, and although he did not live up to his earlier boast to stop Emenike from scoring, he however had the last laugh as he and his teammates walked away from the Olimpiyskiy Stadion Luzhniki with all the points at stake.