Sunderland had taken a 52nd-minute lead with a delightful counter-attack neatly finished by Kieran Richardson's first-time strike into the top corner before Wolves embarked on spirited turnaround in the driving rain.
Facing the prospect of going two goals down at home, Wolves goalkeeper Wayne Hennessey dived the right way to save a Sebastian Larsson penalty in the 73rd minute and his team-mates took less than 30 seconds to fashion an equaliser through Fletcher's firm header.
Fletcher was on target again eight minutes later with a half-volley but Sunderland will feel aggrieved after Wolves midfielder Jamie O'Hara appeared to handle the ball.
The O'Hara incident will be seen by Wolves fans as payback for the penalty given against them when Larsson went down with television replays suggesting the minimal contact Wolves defender Jody Craddock made with him had been outside the area.
"If he didn't touch him, they [Sunderland] got what they deserved," Wolves manager Mick McCarthy told Sky Sports.
The win lifted Wolves to 15th with 14 points from as many games, while Sunderland - being overseen by assistant manager Eric Black while new boss O'Neill watched from the stands after his appointment on Saturday - were left stuck in trouble.
The Black Cats sit one place and one point above the relegation zone and O'Neill, who replaced the sacked Steve Bruce, will have plenty of work to do.
"We do create enough chances, we do get enough balls in the box but unfortunately we don't have anyone there to put it away," Black told Sky Sports.
"There's a lot of good football players out there, there's an exceptionally good team spirit within the squad and I'm sure Martin will galvanise that."
Earlier in the day, Stoke ran out 1-0 winners at Everton thanks to a 15th-minute goal from defender Robert Huth. Stoke Climbed to eighth in the table, two places above Everton.
Manchester City crushed Norwich City 5-1 on Saturday to maintain their five-point lead at the top over champions Manchester United who won 1-0 at Aston Villa.
Tottenham Hotspur beat Bolton Wanderers to stay third, fourth-placed Chelsea won 3-0 at Newcastle United and Arsenal climbed to fifth with a 4-0 victory at Wigan Athletic.
Fulham host Liverpool on Monday.
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