Mario Vrancic was fouled just outside the area by Marco Matias and stepped up to curl the resulting free-kick past Cameron Dawson into the top corner.
The result leaves Norwich five points clear of both Sheffield United and Leeds with three games to play in the Championship.
Marco Stiepermann’s long-range shot gave Norwich a 19th-minute lead at Carrow Road before Fernando Forestieri equalised before half-time with a long-range drive.
Steven Fletcher gave Wednesday a 53rd-minute lead before Norwich saved themselves at the death.
Marcelo Bielsa’s hopes of taking Leeds United back to the Premier League after a 15-year absence through automatic promotion suffered a huge blow with 10-man Wigan beating them 2-1.
A Gavin Massey double saw the tier two strugglers come from behind to silence the 30,000-plus home supporters and leave Leeds third behind Sheffield United on goal difference with three matches remaining.
Sheffield United had earlier moved back into second after emerging 2-0 winners against 10-man Nottingham Forest.
Leeds looked to be well on their way to three points when Wigan’s Cedric Kipre was red-carded for handling the ball on the line.
Even though Pablo Hernandez’s penalty was saved the hosts went 1-0 up soon afterwards with Patrick Bamford scoring.
However, Massey levelled for Wigan a minute before the break with a stunning strike and added a second with a header just after the hour mark.
Massey’s double gives Wigan a five-point advantage over third from bottom Rotherham — who lost 4-3 to Swansea.
Second-half goals from Mark Duffy and Enda Stevens gave Sheffield United a vital win — after Yohan Benalouane received a straight red two minutes into the second half — to end a run of two draws.
“They (Forest) are a good side with an experienced manager so it was good to get in front, close the game out and get back to what we do,” United manager Chris Wilder told Sky Sports.
“It’s been a great effort by everyone and we are not done yet. It’s been a tough week but we came roaring back,” added the 51-year-old Englishman, who was voted Championship manager of the year by his peers.
United had looked blunt up front in a goalless first half with their talismanic leading scorer Billy Sharp sitting out the game with a hamstring injury.
