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.
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