The Tigers were unchanged, while Sam Hutchinson came in for the Owls in midfield.
Fernando Forestieri was fouled by Michael Dawson, who was booked, and from the resulting free kick the Argentinian brough out a good save from Eldin Jakupovic on 10 minutes.
The Tigers goalkeeper was then forced to punch away after a Ross Wallace free-kick.
Hull came closest to scoring on 29 minutes. A mistake from goalkeeper Keiren Westwood gifted Hull a corner, and Dawson saw his effort cleared off the line by Kieran Lee.
Westwood then atoned when he raced out to deny Abel Hernandez as he raced clear on goal.
The Tigers were now on top and Mo Diame saw his effort crash against the post with Westwood beaten.
Next Moses Odubajo tested the Owls defence, who needed half-time to come quickly so they could regroup.
Wednesday could have snatched the lead in first-half stoppage time, but Jakupovic comfortably held Tom Lees header, after Andy Robertson conceded a needless corner.
Backed by superb noise from the Wembley crowd, Wednesday improved after the break but could not break Hull down.
And the Tigers should have gone ahead from a swift breakaway, but Robertson fired wildly over.
But the goal they were threatening eventually came, Diame firing home from long range to break the Owls’ resistance.
Despite finishing the game with four strikers, Wednesday failed to break down Hull’s impressive defence.
Hull: Jakupovic, Odubajo, Dawson, Davies, Robertson, Elmohamady, Livermore, Huddlestone, Snodgrass, Diame, Hernandez. Subs: Bruce, Meyler, Clucas, Maguire, Maloney, Akpom, Kuciak.
Sheff Wed: Westwood, Hunt, Lees, Loovens, Pudil, Wallace, Lee, Hutchinson, Bannan, Forestieri, Hooper. Subs: Marco Matias, Nuhiu, Helan, Lucas Joao, Sasso, Wildsmith, Lopez.
Referee: Robert Madley (West Yorkshire)
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