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The Greek international gave the Bolton supporters plenty to savour with a clinical finish after the Trotters had produced a battling performance at fortress Reebok.
Sam Allardyce's men, buoyed by the 2-0 Premiership win over the Gunners last month, were nothing short of workmanlike and hungry to exact revenge for last season's 1-0 loss to Arsenal in the FA Cup sixth round.
Revenge was sweet for Wanderers, who deserved their victory against Arsene Wenger's out-of-sorts stars.
Having seen the first half end goalless, Stelios timed his run to perfection to meet a Ricardo Gardner cross from the left and Arsenal keeper Manuel Almunia had no chance as the ball flew past his outstretched palm.
Bolton were by far the better side in the first half, although they couldn't convert any of their chances.
Having stemmed Arsenal's flow on the flanks, the home side's midfield worked their socks off to win possession and, from the middle of the park, pressed forward with ease.
However, despite Bolton's early dominance, it should have been Arsenal who took the lead as early as the third minute when Abou Diaby was presented with a glorious goalscoring opportunity.
But from six yards out his shot was charged down for a corner and the visitors were left wondering what might have been. That was the story of the game as Wenger's charges toiled to find a breakthrough.
A beautifully weighted lobbed cross from Ivan Campo found Jared Borgetti in the 12th minute but the Mexican hit-man's header was saved by Almunia.
At the other end, Robin van Persie saw a long-range left-footed free-kick fly wide of the target, before Kevin Davies fired high and wide as Bolton sought the opener.
Gardner had a penalty appeal turned down after a bursting run midway through the first half, while Japanese midfielder Hidetoshi Nakata saw an ambitious volley saved by Almunia.
Jose Antonio Reyes tried his luck from distance, but Bolton shot-stopper Jussi Jaaskelainen wasn't troubled.
As the match progressed Stelios had a good chance to break the deadlock, but the teams were level at half-time.
The resumption saw Reyes fire over the bar from the penalty spot after a brilliant pull-back by Aleksandr Hleb.
On the hour mark substitute Ricardo Vaz Te beat Philippe Senderos at the back post but dragged his shot agonisingly across the face of goal.
Arsenal then had the better of the chances. Fredrik Ljungberg crossed for van Persie, but the Dutchman's header found the crossbar and two minutes later he fired into the side-netting.
Ljungberg had a chance of his own in the 72nd minute but Jaaskelainen produced a brilliant fingertip save to deny the Swede.
Another of Bolton's substitutes, new signing Matt Jansen, saw a shot charged down at the near post.
But cue Stelios who, with a perfectly-timed run, rose tallest to send Arsenal packing and possibly end their chances of silverware this season.