The home side's third goal came courtesy of a back pass from Dickson Etuhu two minutes into the second half that rolled into the net after a paper bag blew in front of Warner as he tried to clear.
Wednesday were already in front thanks to a two-goal first-half blast that ensured a disappointing end to a lacklustre campaign for the Canaries after pre-seasons predictions of a play-off spot.
And even a second-half fightback inspired by Dion Dublin failed to spoil Wednesday's winning end to the season.
It was a bright finish for Wednesday whose impressive end to the season saw them finish ninth - their best since 2000.
After a dreary start, Jermaine Johnson - a £400,000 January signing from Bradford - grabbed his second goal for the club and his first at Hillsborough.
After 26 minutes he found space on the right, swerved inside and slammed an unstoppable left-foot shot out of Warner's reach.
And Wednesday doubled their lead with the last chance of the first half just seconds after Norwich striker Robert Earnshaw was ruled offside when he had a free run at the home goal.
As Norwich manager Peter Grant led the touchline protests, Wednesday produced the second goal.
Kenny Lunt's corner was headed on by Lee Bullen and Deon Burton stole in at the far post to drive in a shot and take his season's tally to 13.
Two minutes into the second half came the oddball third goal before Norwich top-scorer Earnshaw replied with a super volley for his 19th of the season.
And after 75 minutes, former Manchester United and Aston Villa striker Dublin claimed the second with a typical header after switching from his starting position at centre-back.