The Owls brought back Sam Winnall up front to partner Jordan Rhodes, with Fernando Forestieri moving wide and Adam Reach dropped to the bench.
The Owls took the lead after 15 minutes and it owed all to the persistence of midfielder Sam Hutchinson.
He charged the ball down, chased hard into the corner, forcing John Ruddy to make a hash of his clearance.
The ball fell to Ross Wallace who fired home from around 40 yards into an unguarded net.
Forestieri could have made it 2-0 three minutes later, but dragged his shot wide of Ruddy’s goal.
But the Owls did double their advantage on 22 minutes. Forestieri pruduced a teasing cross from the left and Rhodes headed home his second goal in Wednesday colours.
The hosts suffered a first-half setback when Hutchinson limped off, with what looked like a knee injury, and was replaced by David Jones,
Norwich pulled a goal back when Cameron Jerome headed in at the far post on 38 minutes.
But three minutes later, the Owls restored their two-goal cushion as Forestieri’s corner was headed in at the far post by Morgan Fox, the left-back’s first goal in Wednesday colours.