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Dunne turned Steed Malbranque's 25th-minute cross past goalkeeper Brad Friedel to ensure the points remained on Wearside and end the home side's run of five successive league draws.
But Villa would have left the north-east, where they lost 6-0 to Newcastle on their last visit, with something to show for their efforts had striker Emile Heskey not passed up a glorious second-half chance.
Stewart Downing had earlier hit the woodwork and substitute Marc Albrighton forced a good save from keeper Simon Mignolet as the visitors, who had won on their last three visits to the Stadium of Light, staged a late fightback.
However, the Black Cats' resilience, with Titus Bramble once again a rock at the back, provided the foundation for just a second league victory of the campaign in front of a crowd of 41,506.
Sunderland's over-reliance on Darren Bent's goals has become a theme for manager Steve Bruce in recent weeks, and it is not difficult to see why.
Of the 10 goals they had managed before the game, Bent had contributed seven and record signing Asamoah Gyan two, with Stephen Carr's own goal making up the total.
Bruce has challenged the rest of his team to help out on that front, and when they got their noses in front, it was, for once, not Bent who did the damage.
It will have mattered little to the Black Cats that the decisive touch on Malbranque's 25th-minute cross came from Villa defender Dunne, who in the process put own goals level with Gyan as the club's second top scorer.
Up until that point, there had been little between the sides - indeed, the visitors might themselves had been in front had Downing's third minute shot not come back off the foot of the post.
Nigel Reo-Coker had also seen a strong penalty appeal waved away by referee Mark Halsey after he had gone down under the close attentions of Lee Cattermole and Bramble, and Nedum Onuoha's well-timed 16th-minute challenge prevented Stephen Ireland from reaching Heskey's dangerous cross in front of goal.
But once Dunne had inadvertently broken the deadlock, the impetus was very much with the home side, and they might have increased their lead within two minutes.
Ahmed Elmohamady found space down the right and squared for Danny Welbeck, whose first-time shot was expertly palmed away by goalkeeper Brad Friedel.
Elmohamady himself whistled a right-foot effort just wide three minutes before the break after being set up by Bent, and although Villa finished the half with a flurry, Mignolet was rarely troubled.
The Belgian should really have been called into action three minutes after the restart when Heskey turned Michael Turner on halfway and fed the ball into Ireland's run.
However, the midfielder checked inside as he reached the penalty area and the covering Bramble did just enough to dispossess him.
Mignolet was called upon two minutes later after Ashley Young collected Downing's pass and forced a solid save, although as the game became more stretched, the Black Cats were finding space at the other end too.
But Villa were starting to make their presence felt and they went close to an equaliser three times within as many minutes.
First Heskey was dispossessed by the covering Bramble in front of goal, although the former England strike was guilty of a glaring miss seconds later when he completely missed his kick after Downing's cross evaded Mignolet.
The Sunderland keeper then had to claw substitute Steve Sidwell's 63rd-minute header off the line with the home defence struggling to clear their lines.
Mignolet was in action again with 19 minutes remaining to beat away Albrighton's shot, and Dunne hacked a volley across the face of goal seconds later with Villa dominating.
But despite a late flurry, the home side held out to claim all three points with Dunne denying Bent a late strike with a well-timed tackle.