Mick McCarthy's side have now taken seven points from their opening three games, although they were second best during the second 45 minutes on Saturday.
Villa dominated territorially during that period, with Gabriel Agbonlahor causing plenty of problems with his pace while Charles N'Zogbia posed more of a threat.
But skipper Roger Johnson produced a typically rock solid performance at the heart of the Wolves back four to help snuff out the threat of the home side, who also remain unbeaten.
Wolves seldom threatened a Villa defence in which youngster Chris Herd, who replaced QPR-bound Luke Young at right-back, acquitted himself well.
But that will not take away from their satisfaction at the start to the campaign after only escaping relegation on the final day of last season.
Fabian Delph became the first player to be yellow carded for a rash touchline challenge on Matt Jarvis after only five minutes.
Villa's first chance fell to skipper Stiliyan Petrov but the Bulgarian international dragged his 20-yard drive wide.
Shay Given looked to be struggling with his recent groin problem but did well to block a downward Stephen Hunt header from Stephen Ward's deep centre.
Villa came close to taking the lead when the impressive Emile Heskey dragged Agbonlahor's cross just wide at the near post.
Jamie O'Hara should have done better when he curled his shot over the bar after being teed up by Steven Fletcher.
Petrov got into a promising position near the by-line, despite Wolves appealing in vain for offside, but Wayne Hennessey was alert and brave in diving at the feet of Heskey from the resulting low centre.
Herd had half a chance when he was first to react to an N'Zogbia corner but could not keep his header down.
O'Hara was booked in first half stoppage time for chopping down Petrov.
Herd made an encouraging start to the second period and his teasing cross was only just too high for Heskey.
The youngster then headed over the bar from a Petrov corner.
Agbonlahor outstripped Roger Johnson for pace and his low drive was turned aside by Hennessey.
Villa were now in the ascendancy and Kevin Doyle headed a Dunne header off the line from Petrov's corner.
N'Zogbia was looking a threat and his centre created a chance for Herd, whose header was tipped over the bar by Hennessey.
Karl Henry was then yellow carded after 63 minutes for pulling back Petrov.
McCarthy made a double change four minutes later with Kevin Foley and George Elokobi replacing wingers Jarvis and Hunt.
Wolves were caught napping at a short Petrov corner which found N'Zogbia in plenty of space, but he failed to take advantage and dragged his shot wide.
It was N'Zogbia's last contribution before being replaced by Barry Bannan.
Villa were still looking the more likely to score and Richard Stearman was booked after wrestling Agbonlahor to the ground.
Hennessey deflected a low Bent centre away from the onrushing Agbonlahor.
Bent then headed just over from a cross from substitute Marc Albrighton but Wolves held out for a hard-earned point.