The Scottish Premier League champions looked likely to head back to Britain with yet another defeat under their belts in the first half but an impressive second half kept Neil Lennon's hopes of qualifying for the knockout rounds alive.
Sports Mole takes a look back at the 90 minutes of the Group G clash at the Stadion Luzhniki.
On Target: 5
On Target: 6
Was the result fair?
In large, yes. Both sides looked dangerous at times during the 90 minutes but an impressive second-half display from Celtic proved that they deserved to take maximum points from their Russian opponents in Moscow this evening.
Spartak Moscow's Performance
The home side started strongly in the opening half, claiming two corners in as many minutes and their goal threat was always apparent but after losing Juan Insaurralde after he was sent off for bringing down Gary Hooper, damaged the side's attacking options and they looked vulnerable, which Celtic were able to capitalise on.
The Scottish outfit struggled to compose themselves in the early stages of the contest and while they defended well initially, they were unable to force a genuine threat on goal and Gary Hooper looked isolated. After scoring against the run of play, the Hoops grew more confident in attack and they were able to take advantage of playing against 10 men in the second half.
Frenchman Tony Chapron had a relatively positive game but he stop-started the game on a few occasions, which prevented the game from flowing. He also took a long time to issue the red card to Insaurradle as he was unsure of the challenge and had to consult with his assistant referee.
Sports Mole's man of the match
While he was only on the pitch for around 30 minutes, Celtic's James Forrest made an instant impact when he was brought on. Within seconds he launched an attack to get Celtic back into the game and force an own goal, which eventually kick-started the Scottish side to victory.
Dmitri Kombarov will not want to see the replay of Celtic's equaliser to take the scoreline to 2-2 in the second half. A shot from Forrest bounced off the goalkeeper, which hit Kombarov and dropped into the back of the net. While Kombarov may not have been able to stop the inevitable, recording an own goal is never something to be proud of.
Spartak Moscow: The Russian side welcome Benfica to Moscow on October 23 as they desperately search for their first points of the tournament.
Celtic: Lennon's side have the daunting task of taking on Barcelona at the Nou Camp in three weeks' time.