Martin O'Neill's men looked to be cruising home at the break after they had replied to David Vaughan's early own goal with a Craig Gardner penalty followed by Fletcher's impressive one-two.
But after on-loan Manchester United man Angelo Henriquez netted with a far-post header 11 minutes from time, Sunderland needed to show plenty of defensive resolve to retain their advantage, sending Wigan sliding back into the relegation zone.
The early signs were not good for Sunderland, who went behind after just four minutes thanks to Vaughan's comical own goal. Ronnie Stam could barely have met Jean Beausejour's dangerous cross with any less conviction, drilling a weak shot straight into the ground.
Sunderland should have escaped but when James McCarthy flicked the ball into Vaughan, the hapless midfielder could only prod it past Simon Mignolet and over the line. O'Neill's men soon shrugged off the disappointment, although it required a slice of good luck to help them on their way.
For had Stam not slipped under no pressure deep inside his own half, Emmerson Boyce would not have needed to foul Adam Johnson and therefore the free-kick which McCarthy blocked with his elbow as he jumped to defend Sebastian Larsson's shot.
Gardner kept his cool to send Ali Al Habsi the wrong way and, within three minutes, the visitors were in front. New boy Alfred N'Diaye was the architect, peeling out to the left flank before crossing deep to Fletcher, who quickly volleyed home from close range after Al Habsi had repelled his initial header.
None of Fletcher's breakthroughs this season could have been any sweeter than his 10th. Getting the slightest of touches to Gardner's deep free-kick, Fletcher was on hand when Johnson knocked it back to curl home a first-time shot in magnificent fashion as Al Habsi remained rooted to the spot.
Shaun Maloney drifted a shot just beyond the far post not long after the hour mark, by which time Wigan had protested vehemently for a penalty, believing Franco di Santo's shot had been blocked in a similar manner to the way McCarthy was punished for, when referee Anthony Taylor felt otherwise.
The hosts still had hope when Henriquez was introduced and the on-loan Manchester United man quickly netted his first goal in English football as Maloney seized on some slack Sunderland defending and delivered a perfect far post cross.