Steven Fletcher's second-half double ruined new Sunderland manager Martin O'Neill's first look at his team.
O'Neill was in the directors' box as Sunderland looked on course to welcome him with only their third Premier League win on the season after Kieran Richardson put them ahead early in the second half.
The game then changed in a matter of seconds as Wolves were revived with growing anxiety sweeping around Molineux after a sequence of eight defeats in their last 10 Premier League games.
Sunderland were awarded a controversial penalty with 18 minutes remaining when Sebastian Larsson tumbled threatrically under minimal contact from Jody Craddock, giving the Swede the opportunity to effectively seal the win.
Larsson's spot-kick was saved by Wolves keeper Wayne Hennessey as justice was done - and Wolves took advantage to level inside 30 seconds as Fletcher's header beat Kieren Westwood.
The momentum was with Wolves and Mick McCarthy's men confirmed only their fourth league win this term as Fletcher fired low past Westwood with nine minutes left as Sunderland appealed for handball against Jamie O'Hara.
O'Neill starts work at the Stadium of Light in earnest on Monday after succeeding sacked Steve Bruce - and Sunderland's brittle nature under pressure will have already drawn his attention.
And yet O'Neill, who left Bruce's right-hand man Eric Black in charge of team affairs, will also know that Sunderland wasted a perfect opportunity to start his reign with a win, only to squander the chance after Larsson had missed the crucial penalty.
Wolves boss McCarthy admitted he was under pressure to get a result after the recent dismal sequence and rain-soaked Molineux celebrated in style following a real show of character in the closing stages to fashion the win.
O'Neill made a low-key entrance moments before kick-off, flanked by long-time backroom colleague Steve Walford and goalkeeping coach Seamus McDonagh.
And they will have both been impressed by the first-half contribution of Sunderland keeper Westwood, who made two crucial interventions to keep O'Neill's new side on terms.
Westwood was alert to clutch Fletcher's early header after a goalmouth scramble which had Wolves appealing for a penalty as Lee Cattermole appeared to drag down David Edwards.
He made an even more vital contribution as the interval approached, miraculously clawing away Stephen Hunt's point-blank shot as the Republic of Ireland midfield midfield man looked certain to turn in an inviting cross from Matt Jarvis.
Sunderland had moments of their own in a first period short on quality, notably when Ward was forced to scramble Stephane Sessegnon's effort off the line at the conclusion of a sweeping counter attack.
A move of similar quality saw Sunderland go ahead after 52 minutes. Wolves were caught cold on the break as Sessegnon fed Richardson, whose powerful finish deceived Hennessey as it flew in a high at his near post.
O'Neill, sitting high in the stand, barely registered any emotion at Sunderland's first goal since his appointment on Saturday.
Sunderland threatened to punish Wolves further as they pushed forward in search of an equaliser - prompting McCarthy to make a double change by sending on Sylvain Ebanks-Blake and Adam Hammill for Hunt and Kevin Doyle.
Hennessey was called into action when Ji Dong-Won sent in a glancing header. It was the South Korean's final involvement as he was then replaced by Ahmed Elmohamady.
Sunderland were then handed an unexpected chance to wrap up the points in dubious fashion in the 72nd minute. Larsson fell spectacularly with Craddock in close attendance. There was little or no meaningful contact and Molineux erupted in fury as referee Phil Dowd pointed to the spot.
Hennessey provided a measure of justice by saving Larsson's poor penalty - and the scale of the reprieve was emphasised as Wolves equalised within seconds.
Westwood got a hand to Fletcher's header from another fine Jarvis cross, but could not keep it out.
Sunderland, from scenting victory, were now on the retreat and Wolves completed the turnaround with Fletcher's second nine minutes later. The Black Cats claimed handball against O'Hara as the striker took control in the area, but he did not waste time as he shoot low past Westwood.
Wolves now had a precious lead to protect and they did so successfully to ensure O'Neill's takes over a side on the back of a defeat.