Andrey Arshavin cut in from the left to fire in a shot and Samir Nasri volleyed home to put the Gunners 2-0 up.
Ciaran Clark gave Villa hope with an 18-yard strike, although Marouane Chamakh's poked shot for the visitors appeared to have put Arsenal safe.
But Clark nodded in to set up a tense finale before Jack Wilshere's injury-time header secured victory.

The Gunners let a two-goal advantage slip last Saturday when they lost 3-2 to Tottenham and, despite securing another two-goal lead at Villa Park, they looked unconvincing as they almost threw it away again.
Credit, though, must go to a depleted Villa, who went into the game with Gabriel Agbonlahor and Marc Albrighton added to a lengthy injury list but raised themselves after a poor first half to give their opponents a scare.
Arsenal, who were beaten by Braga in the Champions League on Tuesday and lost captain Cesc Fabregas to injury in the process, held on to move briefly to the top of the Premier League, until Manchester United thrashed Blackburn later in the day.
Although the win helped the Gunners improve on the top-flight's best away record, it remains to be seen whether it will translate into a firm title push.
Arsenal have flattered to deceive too many times this season, digging out hard-fought wins at Blackburn and Everton only to shoot themselves in the foot with home defeats by West Brom, Newcastle and Tottenham.

606: DEBATE Well Arsenal manage to win a game despite our best efforts to throw it away Dave Masala

Against Villa, Arsenal's performance encapsulated their season to date as they quickly got into the groove of producing their pretty patterns of eye-catching football but then relinquished control of the game.
Villa left-back Stephen Warnock was almost punished for giving the ball away in the opening minute when Arshavin put Chamakh through before home keeper Brad Friedel came to his team-mate's rescue by blocking at the striker's feet.
Tomas Rosicky flashed a shot across goal and Nasri sent a drive just wide as Arsenal picked and probed at Villa.
The home side were struggling but almost punished the visitors for their profligacy when Clark flicked on a Stewart Downing cross for Ashley Young at the far post but the winger - seemingly from an offside position - fired over from close range.
It was a rare sight of goal for a Villa side that was spending most of the time trying to keep Arsenal at bay and the pressure finally told when James Collins and Luke Young both missed a clearance.
Arshavin gathered possession on the left flank before driving at goal and angling in a shot, which Friedel got a hand to but could not keep out.
Immediately after, Nasri rounded Friedel before shooting into the side-netting before atoning for the miss when he volleyed home Arshavin's corner from the edge of the area via a Luke Young deflection.
Arsenal were denied a third when Chamakh had a header brilliantly kept out by a reflex save from Friedel before the home side, who took off ex-Gunners star Robert Pires at half-time, came out and went at Arsenal after the break.
They were rewarded when Clark chested down a Sebastien Squillaci clearance and powered in a shot, although Villa striker John Carew was in an offside position blocking Gunners keeper Lukasz Fabianski's view.
Rosicky played Chamakh through to restore Arsenal's two-goal cushion only for Clark to renew Villa's hopes of preserving their unbeaten home record by nodding in off the crossbar after Richard Dunne's header across goal from a corner.
A shaky Arsenal had to show their dogged side to hold on to their lead and confirmed their win when Chamakh picked out an unmarked Wilshere to head in from point-blank range for his first Premier League goal.