It was a tale of two halves at Molineux as second-half goals from Hwang Hee-Chan and Spanish defender Pau Torres saw both sides leave with a point.
Gary O'Neil's men came into the weekend with renewed belief after stunning Manchester City to a 2-1 victory to hand the reigning champions their first league defeat of the season last time out.
Aston Villa, on the other hand, made it three straight league wins last weekend when they steamrolled Brighton & Hove Albion 6-1 at Villa Park before getting their Conference League campaign up and running with a slender 1-0 victory over Zrinjski Mostar on Thursday.
Wolves named an unchanged starting XI from the win over Manchester City, while Unai Emery made one change to the side that beat Brighton, bringing in Douglas Luiz for Italian forward Nicolo Zaniolo.
It was a drab first half at Molineux, with Aston Villa coming close to an opener in the seventh minute when Matty Cash was denied by Jose Sa in the Wolves goal after the Polish full-back connected with John McGinn's searching cross.
Wolves' best chance of the first half fell to Rayan Ait-Nouri shortly after the half-hour mark, but the 22-year-old drilled his shot wide of the target shortly after connecting with a brilliant cross from Hwang,
With both sides successfully cancelling out each other's efforts in the first period, the second half kicked off with the Villans nearly breaking the deadlock after Ollie Watkins's effort was kept out by another brilliant save from Sa.
It was Wolverhampton Wanderers who grabbed the breakthrough, with Hwang picking up where he left off against Manchester City to hand the hosts a 53rd-minute lead.
Pedro Neto, who has been on song for Wolves this season, beat his marker down the right flank and his cross found Hwang, who tucked home his fifth consecutive Premier League goal on home turf.
However, Emery's side kept their cool and forced their way back into the game 180 seconds later, with Torres showing great composure in the box to beat Sa and restore parity.
Watkins, who recently put pen to paper on a new long-term contract, was pivotal in the Aston Villa equaliser as his dangerous cross was met by Torres, who did well to grab his first goal in a Villa shirt.
Neto came close to putting the hosts ahead with 12 minutes left, but the Portuguese forward failed to keep his effort down from 10 yards out after connecting with a dangerous cross from substitute Sasa Kalajdzic.
With 12 minutes added in stoppage time, Wolverhampton Wanderers had to grind out the game with 10 men after midfielder Mario Lemina was sent off in the 94th minute for picking up his second booking of the game.
Having the numerical advantage, Aston Villa charged forward in search of a fourth straight league victory, but Zaniolo dragged his effort wide after being found at the back post by Leon Bailey before Ezri Konsa fired his shot straight at Sa.
There was late drama when Watkins almost snatched it at the death for Emery's side, but the Englishman's header crashed into the base of the post.
Wolves have now risen to 14th place in the Premier League standings, four points above the bottom three after eight matches, while Aston Villa have now picked up 16 points from a possible 24 to sit level with sixth-placed Brighton & Hove Albion.