The visitors kicked off and the impressive Jermaine Pennant caused problems from early on and throughout the game.
For the home side Leon McKenzie did well to release Ashton but he allowed the ball to run through to Maik Taylor.
Walter Pandiani's shot deflected off Thomas Helveg and bounced over via Robert Green's crossbar.
After a long spell off Blues possession McKenzie made a good run towards the Blues penalty area but then scuffed his shot.
David Bentley tried unsuccessfully to volley home Ashton's deep cross from the left wing.
Stan Lazaridis limped off in the 20th minute to be replaced by Stephen Clemence. He was followed on the half hour by Johnson for his attack on Helveg in an off-the-ball incident.
Briefly Norwich looked more lively, but it was Emile Heskey who came closest to scoring when he got his head to another dangerous cross from Pennant.
Norwich got their goal just before half-time when Kenny Cunningham tripped Darren Huckerby and Ashton sent Taylor the wrong way with a low right-foot shot to the keeper's left.
In the opening minutes of the second half McKenzie fired wide and Ashton's shot was well saved by Taylor.
Blues then enjoyed most of the possession in spite of being down to ten men. Bentley's free-kick went straight to Taylor and Huckerby curled his shot just over the bar.
Taylor made a point-blank save from McKenzie and half-time sub Clinton Morrison hit the cross bar with a fierce shot and headed just over in another Blues attack.
The home side held on to clinch victory and the Canaries fans cheered their team on a lap of honour and got another boost when they heard Southampton had scored a later equaliser against Crystal Palace.
Man of the Match: Dean Ashton - Not just for keeping his cool to tuck away the penalty, but for his non-stop running up front, his ability to hold up the ball and not least his defensive headers when Norwich were pushed back for long periods.