Marco Matias, in his fifth season at Hillsborough, and one-time record signing Adam Reach got the goals as the Owls saw off another club to have fallen on hard times in recent years.
The assists came from Steven Fletcher and Barry Bannan, as Jos Luhukay’s men booked a Carabao Cup second round tie at home to Wolverhampton Wanderers.
It was a deserved victory, Reach probably the pick of several in blue and white who had a good night in the North East.
League One Sunderland battled hard and had their moments in a first half in which the visitors took a while to get going.
But, come the final whistle, there could be few complaints from the home fans at their side’s involvement in the Cup being ended by a side featuring Alex Hunt, a teenager born 15 days after Wednesday last played in the top flight fixture.
He lasted only until half-time but the midfielder’s presence still shone a light on just how long the Owls have been out of the Premier League.
Just when Wednesday will have a chance of reclaiming that place at the top table of English football remains to be seen.
Two near misses have left the club with problems, a Football League transfer embargo meaning there have been no signings since last January.
There have been suggestions in recent days that this may soon be lifted but, even without any new additions, this is a squad that boasts plenty of strengths.
Playing out from the back, however, is not one of them and yet that was what the Owls tried to do time after time in the first half against their League One hosts.
It was a risky strategy, not least because Sunderland quickly caught on to the visiting defence’s vulnerability in possession and pressed the ball high up the pitch.
That Wednesday weren’t punished in those opening exchanges was down to the home side’s final ball being poor and their finishing even worse.
Elliot Embleton dragged a shot wide when well placed, while Luke O’Nien was far too slow when found unmarked on the edge of the Wednesday six-yard box with the goal gaping.
His hesitation allowed Joost van Aken to scramble back and divert the eventual shot behind for a corner.
Wednesday’s tendency to over-play at the back was made all the more nonsensical by how the opening goal came about.
Route one was the order of the day, Joe Wildsmith’s punt forward being flicked on by former Sunderland striker Fletcher.
Alim Ozturk was still the favourite to reach the ball as it landed in the home penalty area but Matias had other ideas by nipping in and rolling a shot past former Bradford City goalkeeper Jon McLaughlin.
Ozturk, who had a wretched night, was at it again 10 minutes after the restart with an attempted clearing header that merely went straight up in the air.
Matias quickly swooped to fire a shot that Jack Baldwin did very well to head off his own line.
Wednesday spurned another chance moments later when Reach’s first touch took him wide enough for McLaughlin to race from his line and block the shot.
Sunderland, like in the first half, had their moments after the restart.
George Honeyman fired high and wide for the hosts, while Josh Maja got himself in a tangle on the edge of the area when a shot was on.
But justice was done 11 minutes from time when Reach ghosted in to meet a Bannan cross with a flicked header to beat McLaughlin and kill off any hopes of a Black Cats comeback.
Sunderland: McLaughlin; James (Molyneux 80), Ozturk, Baldwin, Hume; Cattermole (Maja 66), O’Nien; Power, Honeyman, Embleton (Gooch 61); Maguire. Unused substitutes: Ruiter, Robson, Mumba, Taylor.
Sheffield Wednesday: Wildsmith; Nielsen, Lees, Van Aken (Penney 63); Palmer, Bannan (J Lee 86), Hunt (Kirby 46), Boyd; Matias, Fletcher, Reach. Unused substitutes: Dawson, Jones, Nuhiu, O’Grady.
Referee: B Toner (Lancashire).