Bradford lost away from home for the first time this year as Norwich recovered from a one-goal half-time deficit to claim a hard earned three points.
Left-back Adam Drury fired in the first shot of the game but although it took a deflection off a defender referee Mr Joslin awarded a goal-kick.
In the 14th minute there was a scare for the home side when Ben Muirhead crossed from the right and Laurens Ten Heuvel crashed a header across the crossbar.
Four minutes later Muirhead was inches away with a rising drive after creating space just inside the Norwich penalty area.
There was a chance for Norwich when Aidan Davison dropped Clint Easton's corner but the keeper fell on the ball to deny a shooting opportunity.
On the half hour Claus Jorgensen crossed from the left but Ten Heuvel headed straight at Robert Green.
Gary Holt was booked for a challenge on Muirhead and after Dave Wetherall had headed Jorgensen's free-kick into Green's arms Mark Bower was booked for a foul on David Nielsen.
Bradford took the lead four minutes before half time when Jorgensen's left-wing cross bounced off Darren Kenton to set up Danny Forrest, who placed a low right-foot shot into Green's net.
Mark Rivers spurned the chance of an equaliser just before the half time whistle when he headed wide after Darel Russell's shot rebounded off Davison's legs.
Rivers made up for this miss four minutes into the second half when he sent Davison the wrong way with a low right-foot penalty.
Zema Abbey put Norwich ahead in the 54th minute when he collected Steen Nedergaard's pass 22 yards out and curled his right-foot shot beyond Davison's despairing dive and into the top left-hand corner.
Russell was unlucky to concede a penalty when he caught Muirhead with a follow through, but Jorgensen's right-foot shot went high into the net as Green dived to his right to make the scores level with 22 minutes left.
Holt picked out Rivers with a quickly taken free-kick and the Canaries winger deceived Davison with a low left-foot shot to keep alive play-off hopes for the East Anglians.