The game was devoid of clear-cut chances until Scotland international Fletcher picked up a loose ball and fired home from 25 yards just after the hour mark.
Wednesday then had chances to wrap up the points, but were comfortable - even with six minutes of stoppage time - to run out 1-0 winners.
Owls caretaker manager Steve Agnew said: “I’m really pleased with the result, [it was] three points that we needed and on the balance of play we deserved to win by more than one goal.
“I said at half-time that I thought we were the better team without having had too much of a threat on goal, but then we upped our game a touch.
“We pressed high, we worked them. I can’t remember too many times that Keiren [Westwood] had much to do.”
Goalkeeper Keiren Westwood and midfielder San Hutchinson returned after missing the midweek FA Cup tie at Luton, along with Marco Matias, while fit-again Lucas Joao was named as a substitute.
The Owls had a couple of early sniffs at goal, Fletcher's shot deflected wide for a corner, and the resulting low cross from Matias nearly catching out Jamie Jones in the Wigan goal.
Wednesday had their first penalty appeal waved away when Adam Reach raced clear, only to be denied by Cheyenne Dunkley's recovering tackle, before Fletcher's long-range shot had Jones scrambling to claw the ball away.
But it was the visitors who came closest to a goal in the opening half. Anthony Pilkington's header from a corner zipped across goal, but Joe Garner was unable to make enough contact to force the ball over the line.
Referee Peter Bankes dismissed a second penalty appeal in first-half stoppage time when Fletcher's fierce shot was blocked by Cedric Kipre.
Josh Windass's long range effort failed to trouble Westwood as a low-key opening 45 minutes ended in stalemate.
Both sides were dealing in half chances, the best Wednesday could muster were blocked shots from Reach and Fletcher, the latter also having a tame header which failed to test Jones.
The introduction of substitute Lucas Joao finally broke the deadlock, but it was Fletcher who netted with a fine long-range striker on 62 minutes.
Joao played George Boyd in, but the midfielder was denied by a goalmouth block, before substitute Atdhe Nuhiu failed to poke the ball home after another scramble inside the box.
Wigan boss Paul Cook said: “At half-time I was thinking there was something there for us, but in the second half Sheffield Wednesday totally dominated the game and fully deserved the victory.
“We got ourselves into a position to possibly get something from the game but, unfortunately, we fell away in the second half and Sheffield Wednesday were full value for the win.
“We never got a foothold in the game or got into positions to hurt them and that is great credit to them.”