Fabrice Muamba scored for The Trotters before goals from Andrey Arshavin and Chu-Young Park sealed victory for the home side.
The Gunners will join Manchester United in the draw for the next round, as Arsene Wenger looks to end the six year spell without silverware.
Bolton boss Owen Coyle stated that he felt his side were unlucky however, and felt they should have been awarded a penalty when Emmanuel Frimpong seemed to impede Gary Cahill.
“We have lost the game 2-1. I don’t think there is anybody who was here tonight who would recognise it,” the Scot told Sky Sports after the game.
“We certainly, I feel, created the clear opportunities and should have been in the next round of the cup. But we’re not and that little bit of luck is going against us just now.
“We had a stonewall penalty in the second half not given as well, which doesn’t surprise me.
“Coming to the Emirates, we have not really had much fortune over the years.
“But the lads stuck to their task, created loads of goalscoring opportunities and, as I say, Lady Luck never shone on us tonight,” he concluded.
Bolton travel to take on Swansea at the Liberty Stadium next, while Arsenal have a London derby against Chelsea at Stamford Bridge on Saturday.
By Gareth McKnight