Chris Eagles equalised after superb work from Fernando Guerrero but Colace sealed it from De Silva's cross.
Clarke Carlisle headed Burnley in front from a Chris Eagles cross early on, but Robert Taylor levelled from six yards.
Former Canaries loanee Dean Marney had given the hosts a lead on 33 minutes after good work by winger Chris Eagles.
The Clarets quickly threatened to extend their lead after hitting Villa on the break but the move was undermined by a poor pass from Chris Eagles.
Owen Coyle's side, inspired by the outstanding Chris Eagles and Kevin McDonald, more than matched Arsenal for long periods and looked the more likely winners for spells in the second half.
Burnley fought back with a goal created by Fernando Guerrero and scored by Chris Eagles, but Hugo Colace scored a bullet header with 15 minutes remaining to settle the tie.
Blake had supplied the delivery for the opening goal and delivered a corner that the unmarked Andre Bikey disappointingly headed wide while Chris Eagles forced a save from Friedel with a low strike.
Substitute Luis Jimenez made it 5-0 with another penalty, then Steven Fletcher's late double gave Burnley some consolation before Steven Caldwell was sent off in time added on before Chris Eagles then netted a third.
Chris Eagles had already signalled that he was in the mood to give Gareth Bale a torrid time, and he skipped away from the defender to cross for Paterson to turn in the simplest of finishes.
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Referee Chris White awarded a penalty try after an Eagles infringement in the 52nd minute and Keatley added the points to make it 20-0.
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