Vela opened the scoring in the 25th minute with a brilliant individual goal
Arsenal coasted through to the FA Cup quarter-finals after demolishing recent Cup giant killers Burnley with three goals of the highest class.
Carlos Vela hit the first with a superb lofted chip in the 25th minute after racing away from three defenders.
Eduardo added a second after the break, converting Alexandre Song's cross with an unorthodox volley off his ankle.
Emmanuel Eboue crashed home a third late on and the improving Gunners will host Hull for a place in the last four.
Having beaten three Premier League teams this season on their way to the Carling Cup semi-finals - including the Gunners - Burnley came into the match confident they could inflict a first defeat in 16 matches on Arsenal, whose momentum is now gathering pace.
Home boss Arsene Wenger, a football purist who preaches the merits of an open attacking approach, even had words of praise for the way Owen Coyle's team play the game.
But, as the teams met for the third time in two seasons, the Championship side were largely outclassed.
An Arsenal side not at full-strength first threatened five minutes in when Andrey Arshavin, yet to score for the north Londoners, dropped deep cleverly before slotting in Vela but the ball just ran away from the young Mexican striker.
When in possession, Burnley - who had only lost one game in their past eight matches - looked good on the ball but Arsenal mostly dominated the play.
After Chris Eagles had whipped in a dangerous cross for the visitors, Arsenal regained their composure and scored with typical class to make the breakthrough.
In the 24th minute, Arshavin gave a simple pass to Vela just inside Burnley's half, and the rest was a blur of brilliance.
The Mexican let the ball run across his body then drew a posse of opponents towards him before pushing it through the legs of a prone Clarke Carlisle and accelerating towards goal.
With Burnley defenders trailing in wake and racing back to catch him, Vela coolly produced an outstanding finish, looping the ball high over the onrushing Brian Jensen with his left foot.
Arsenal could have doubled their lead in the 37th minute when Song floated a clever ball over for Vela but, as he took it down on his chest, Carlisle made a desperate saving tackle before he could shoot.
Caldwell then had to make a similar saving tackle from the sometimes rusty-looking Eduardo but Burnley did then give Arsenal a scare as Lukasz Fabianski failed to clear a corner.
But Arsenal made their dominance pay five minutes after the break with another goal of top-class individual quality.
With Burnley failing to clear a corner, Song chipped a perfectly timed ball over their back-line and Eduardo - just onside - flicked a creative first-time volley into the top corner with the ankle which he broke so badly last year.
Theo Walcott came off the bench to make his first Gunners appearance in over four months following a shoulder injury.
Arsenal right-back Bacary Sagna whipped in an accurate cross for Eduardo, but the Croatian international nodded wide with the goal gaping.
Walcott was then played in by Arshavin in the 76th minute but, one-on-one from 12 yards out, he pushed the ball into Jensen's body.
But Arsenal turned the screw in the 84th minute when William Gallas' clever pass found Song who backheeled for Eboue who ran onto the ball and smashed a finish past Jensen into the bottom corner.
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