The Owls were full value for the win, with further goals from Fernando Forestieri and Frerico Venancio securing all three points at Hillsborough.
Owls captain Glenn Loovens - whose contract will not be renewed in the summer - came in at the heart of defence for Tom Lees, who dropped to the bench.
There was also a start for Academy youngster Ash Baker, starting at right wingback.
Forestieri had a great chance to open the scoring, but scuffed his shot wide after good work from Lucas Joao and Atdhe Nuhiu.
But the latter was on the scoresheet after 14 minutes, heading in at the back post after a teasing cross from Adam Reach - the Owls' player of the season.
Nuhiu - out of contract in the summer, but mulling over a new deal - has been a key player under Jos Luhukay, and Wednesday are keen to secure his services for next season.
It was the 28-year-old's 12th goal of the season - all but one of those coming since Luhukay arrived in January.
Christoph Zimmermann's slack back pass gifted a chance to Forestieri, who slotted the ball beyond a stranded Angus Gunn to make it 2-0 after half an hour. It was his fifth goal in eight games, after missing most of the season through injury,
Loovens was given a standing ovation as he made his Hillsborough farewell - subbed for youngster Jordan Thonriley just before half-time. It was an emotional moment for the 34-year-old Dutchmanm, who had spent the last five seasons at S6.
Nelson Oliveira should have reduced the deficit after hakf-time, but totally fluffed his header unmarked from eight yards out.
Gunn was at full stretch to deny a Forestieri free-kick, but two goals in quick succession made it 4-0.
First, defender Venancio volleyed home from Reach's cross, then a mix-up between the Canaries defence and Gunn allowed Nuhiu to tap into an unguarded net.
Venancio is on a season-long loan, and this could be his final game, with the Owls yet to decide if to try and make the deal permanent in the summer. "Sign him up" was the Kop's chant.
Norwich spurned several chances to net a consolation goal, before Timm Klose swept the ball in on 83 minutes.
Gunn denied Wednesday a fifth goal with two smart saves late in the game.
First he rushed out to deny Forestieri, before producing a stunning save to keep out Nuhiu's header.
But there was no denying Nuhiu his hat-trick, netting a stoppage-time penalty after Forestieri was fouled in the box.