The Bhoys progress to the next stage of the competition for the first time in five seasons after a vital win in their 150th game in the European Cup.
A first half strike from Gary Hooper and a second-half Kris Commons penalty secured the win after a tense night of football in Glasgow.
The opening stages of the game were tetchy and evenly contested, with neither side establishing much of a stronghold on the contest or creating many clear chances, until Spartak midfielder Kim Kallstrom caused Celtic heart’s to flutter a little after a quarter of an hour when he played a neat one - two on the edge of the area, before placing his left foot shot narrowly wide of Fraser Forster’s post.
With Brazilian striker Emmanuel Emenke looking lively for the Russian side, it looked like Celtic would be set for a night of struggle, however not for the first time in this season’s competition the club showed its clinical side.
Greek striker Georgios Samaras picked up the ball on halfway and weaved past several Moscow players before launching a long ball up field which was poorly controlled by defender Juan Insaurralde and Hooper pounced to lash the ball first time past the helpless goalkeeper.
Celtic had a few more half chances as the first half wore on, however Spartak came back into the contest and when the equalizer came it was hardly against the run of play.
Standout man Emenke was once again at the center of the action as he shrugged off a challenge in central midfield and drove the ball forward before feeding Ari on the right side of the box, and the Brazilian nonchalantly chipped the ball over Forster for the equalizer.
That was the last major drama of the first half, but five minutes into the second period Celtic came within a whisker of going back in front.
Right back Mikael Lustig did well to find some space on the right flank as he put in a decent cross which was met on the half-volley by Samaras. His shot cannoned off the post with Spartak goalkeeper Sergei Pesiakov well beaten.
That looked like being the best chance the club was going to have, however, with the home side mindful not to get carried away with chasing the game, wise in the knowledge that losing the game would certainly put it out of the tournament.
On 80 minutes Celtic did get the goal it needed when Samaras went down in the box under very minimal pressure.
Kris Commons stepped up and thumped the ball in via the underside of the crossbar to secure the victory, and Celtic’s passage into the knockout stages, with a late Kallstrom red-card aiding the cause even more.