Arsene Wenger's men put their recent woes behind them to complete a stunning turnaround at the Emirates, thanks to a devastating second half performance.
Three goals in a destructive 10-minute spell turned the game on its head, as Villa deservedly lead at the break thanks to goals from Richard Dunne and Darren Bent.
Arsene Wenger’s side, which had previously lost its last three games in all competitions, appeared to be on course for another miserable day until two Robin Van Persie penalties and a Theo Walcott effort rescued the day and eradicate the recent woes.
Both teams named strong sides for the encounter, with Alex Oxlade-Chamberlain and Robin van Persie starting for the home side, while Thierry Henry, whose goal dispatched Leeds United in the previous round, had to be content with a place on the bench.
LA Galaxy loanee Robbie Keane continued up front for the visitors following his impressive two-goal haul against Wolves in the league last weekend.
Lukas Fabianski also started in the Arsenal goal in place of regular first choice keeper Wojciech Szczesny.
The home side started brightly, with a short free kick leading to Thomas Vermaelen rifling a ferocious 30 yard effort that Shay Given palmed over at full stretch.
Minutes later, Tomas Rosicky’s through ball sent Walcott racing through on goal, but the England international got it all wrong as he skewed horribly wide.
Villa briefly responded when Alan Hutton’s cross found an unmarked Bent, but the Villans' top scorer hesitated as Fabianski charged out of his goal, even though the striker was first in line to reach the ball.
Although Arsenal looked the more comfortable team in possession, it failed to create any end-product and was punished for the lack of urgency just after the half hour mark.
A short-corner routine lead to Keane clipping the ball into the box, and Dunne rose highest to power a header into the top corner and give the visiting side the lead.
Arsenal instantly fought back when Rosicky’s tame shot was spilled by Given, but the Irish keeper gathered the loose ball.
Alan Hutton then carelessly lost the ball in his own box, but Ramsey couldn’t beat the keeper once more from a tight angle.
After Oxlade-Chamberlain saw his ferocious effort saved, Villa capitalized by racing up the other end to double the lead with a classic breakaway goal that exposed the flaws in the home side's brittle defense once more.
Bent, who had scored six goals in his last eight appearances against Arsenal prior to this fixture, continued his good record against his boyhood club by running onto Stephen Ireland’s precise through ball and clinically tucking the it home from a tight angle after Fabianski had saved his initial effort.
Arsenal came out a re-energized side after the break, and was unfortunate not to instantly pull a goal back when Per Mertesacker’s header was cleared off the line by Ireland. The home side handed itself a lifeline soon after when Ramsey won a penalty after being sinically felled by Dunne in the area.
Van Persie stepped up to coolly send Given the wrong way and dispatch his 24th goal of the campaign.
The turnaround was completed moments later when Hutton’s goal line clearance fortuitously struck Walcott and bounced into the net after the winger had initially tricked his way through the defense and seen his low shot blocked.
The astonishing turnaround was completed when referee Michael Jones awarded another blatant spot kick. Laurent Koscieleney’s surging run was brought to a halt by Bent, with Van Persie emphatically converting into the roof of the net.
Arsenal had further chances to extend the lead, with man-of-the-moment Van Persie looking to seal his hat trick by testing Given once more and narrowly blazing Walcott’s cut back wide.
Villa also wasted a good chance to equalize. Ireland’s pacey cross was met by the head of Ciaran Clark, but Fabianski gratefully clung onto the ball.
But the Gunners held on for the win and sealed a trip to the next stage of the competition to face either Sunderland or Middlesbrough.