A late first half goal from Ross Stewart saw Sunderland edge out the Owls at a raucous Stadium of Light.
This play-off semi-final first leg had all the ingredients for a thriller but never quite came to the boil.
Only once did the lid come off on Wearside, when Stewart made the vital breakthrough to leave the tie delicately poised going into the second leg at Hillsborough on Monday.
The expected fiery start duly unfolded and spawned half chances at both ends – Lee Gregory stabbed wide for Wednesday before Patrick Roberts warmed the gloves of Bailey Peacock-Farrell from distance.
But the game then settled into more of a cagey affair, during which time the respective rearguards gave little or nothing away.
Both defences were well-drilled, robust and organised, leaving teammates higher up the pitch to feed on the merest of scraps.
Peacock-Farrell tipped a deflected Lynden Gooch cross over the bar, which seemed the busiest the keeper would be as the clock ran down on the opening 45.
But right on the stroke of half time, Sunderland broke the deadlock from nowhere. A long punt upfield from a Wednesday corner saw the onrushing Stewart pick the pocket of Sam Hutchinson and the hitman advanced to slide home at the second attempt after Peacock-Farrell diverted the initial shot.
The goal gave the hosts a huge boost and Alex Prichard went within a lick of paint of doubling the lead straight after the restart, curling a clever hit from 20 yards against the frame of the goal.
Wednesday had their backs to the wall and Peacock-Farrell stretched to tip another effort from Prichard before Dennis Cirkin missed a gilt-edged chance, heading off target from close range.
The Owls introduced Josh Windass from the bench but still Sunderland attacked and Hutchinson did well to thwart Roberts with a last-ditch challenge in the box.
Wednesday had a promising spell midway through the second half that led into the closing stages, keeping the ball in the final third, albeit without forcing Anthony Patterson into a save.
And try as they did, the Owls just couldn’t find that ruthless edge, and the Black Cats take the most slender of advantages into a potentially fascinating return tie in S6.
Wednesday: Peacock-Farrell, Palmer, Storey, Dean, Hutchinson, Johnson, Luongo, Byers (Dele-Bashiru 88), Bannan, Berahino (Windass 56), Gregory