Gabriel Agbonlahor saw his first-half effort cancelled out by Michael Kightly, but a spectacular volley from Matthew Lowton and a stoppage-time strike from Christian Benteke enabled Villa to see off a Stoke side who continue to struggle in 2013 and find themselves just four points clear of the Premier League trapdoor.
Villa bossed the early exchanges, but it could have been different had the hosts been awarded the penalty they wanted after barely two minutes when Jonathan Walters smashed the ball into Nathan Baker's arm from close range.
Referee Mark Clattenburg deemed the contact unintentional, much to Potters boss Tony Pulis' obvious disgust on the sidelines. Whether awarding a spot-kick or not might have been harsh on Baker, it was still a let-off for the defender, whose shaky start continued as Kenwyne Jones muscled past only to blaze over.
Stoke looked up for the fight at that point but their optimism was pierced after just nine minutes as Lowton and Jordan Bowery combined from a throw-in to cut through the home defence. Lowton reached the byline all too easily and pulled back for Agbonlahor in front of goal and the striker rolled in at the second attempt after his initial effort was blocked.
The goal came against the run of play but it completely changed the game's momentum and Stoke had an escape when Robert Huth backed off and Bowery fired into the side-netting.
The anxiety among the home fans was obvious and alarm bells were ringing again when Andreas Weimann broke clear and struck the post with a low shot Begovic may have brushed with his fingertips.
Stoke managed to toughen up before the break but created no meaningful opportunities and were booed off by a concerned crowd at half-time.
A badly misplaced pass by Marc Wilson brought more jeers, but it soon became apparent the Republic of Ireland international was injured and he hobbled off. Pulis took the opportunity to strengthen his attack but ignored the claims of former England pair Michael Owen and Peter Crouch on the bench and sent on Cameron Jerome.
That brought a change of shape but it was some time before it started to yield greater end product as Villa continued to dominate play in an increasingly scrappy contest.
Stoke were, however, soon to enjoy their best spell of the game and, with confidence growing, Walters raced away down the left. He fed inside to Charlie Adam, who had been on the field just a matter of minutes, and he in turn teed up half-time substitute Kightly to stab home.
The equaliser transformed the atmosphere and the crowd finally began to find their voice.
But it was not to last as Lowton dramatically swung the game back in Villa's favour with a superb volley three minutes from time. The defender chested down an attempted clearance from a corner outside the box and fired back into the top corner.
Home hopes were deflated and, as the game ran towards injury time, Benteke raced through and calmly stroked the ball past Begovic for the third.