The Bhoys won away from home in the UEFA Champions League for the first time since 1986 thanks to the Greece forward's dramatic late winner after Juan Insaurralde's red card.
Gary Hooper gave Neil Lennon's team the lead, but two tap-ins from Emmanuel Emenike put the home side in front. The game changed, however, when Juan Insaurralde was sent off for a challenge on Hooper and Dmitri Kombarov sent the ball into his own net to level the score after James Forrest had been denied at the end of a sweeping attacking move.
Samaras rose to head home Emilio Izaguirre's header as Celtic sealed a long overdue away victory in the Champions League. The Bhoys last won away from Glasgow in European championship play in 1986, and Lennon would be drawn only so far as to say that he hoped his team could make the game in Moscow "competitive" while acknowledging that the Russian top flight was in a stronger state than its Scottish counterpart.
That assessment looked accurate in the early stages but Spartak's attacking approach left gaps for the visitors to exploit. They did that to great effect when Victor Wanyama initiated a move that ended in Hooper sweeping home Mikael Lustig's low cross.
The breaks kept coming for Celtic ,but, in the meantime, Spartak cranked up the pressure itself. Dani Pareja's free-kick was well-saved by Fraser Forster, but the goalkeeper could do nothing to stop Emenike, who tapped home after Ari had sent Kallstrom's superb long pass behind Kelvin Wilson across goal.
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Shortly after the halfway point the turnaround was complete. Again, Ambrose and Wilson were too slow to react when the ball got behind them, this time as a result of an Ari shot that was parried weakly by Forster. Demy de Zeeuw pounced and slid the ball across goal for Emenike to touch over the line.
Hooper, though, continued to threaten and was brought down when through on goal by Insaurralde after racing on to Charlie Mulgrew's pass. After initially seeming to ignore the challenge, referee Tony Chapron finally produced a red card for the Argentine defender following the disbelieving protests of the Celtic players. Mulgrew, however, could only direct the subsequent free kick straight at goalkeeper Sergei Pesyakov.
It was not long, though, before Lennon's team made the man-advantage count. Mulgrew's low cross from the left was dummied by Samaras and passed on by Hooper for substitute Forrest to shoot. The winger's effort was saved by Pesyakov but rebounded into the net off of Kombarov.
Celtic had time to mount one last attempt, and when Izaguirre lifted a left-footed cross into the center of the penalty area in stoppage time, Samaras rose superbly to head across goal and seal a memorable victory.