A first-half Dean Ashton penalty boosted Norwich's Premiership survival hopes against 10-man Birmingham.
The visitors had dominated play for the opening half-hour and should have converted any of a number of chances.
But the game turned when Damien Johnson was sent off for punching Thomas Helveg in the ribs in the 31st minute.
Norwich made that advantage count in the 45th minute when Kenny Cunningham brought down Darren Huckerby, and then held on in a scintillating second half.
Birmingham had looked far more likely to open the scoring, with Walter Pandiani arguably the biggest threat with three shots in the first half.
He fluffed his first two efforts, while his third - in the 25th minute - was on target but steered away for a corner.
Birmingham's best chance of the half, however, came a minute later but Matthew Upson headed over the bar when completely unopposed.
All the Midlands side's early dominance, however, was wasted when Johnson was given his marching orders for his clash with Helveg.
Fifteen minutes later, the darting Huckerby won Norwich's penalty, which Ashton coolly slotted past Maik Taylor.
The former Crewe striker came close to adding a second moments after the interval but Taylor cut out his drive.
With a one-goal lead, Norwich intially were content to retain possession, while Birmingham did their utmost to level the scores.
Emile Heskey nearly levelled when clear to head the ball home but strike partner Clinton Morrison, on for Pandiani, handled the ball in the box.
There then followed a brief lull in the game as both sides faded before a captivating final 20 minutes of end-to-end stuff.
First, Leon McKenzie found himself in a perfect position to put the game out of Birmingham's reach with 10 minutes left.
Huckerby, a handful all afternoon, landed a perfect cross to the boot of McKenzie but his effort was blocked by a superb Taylor reflex save.
Seconds later, Stephen Clemence was left pondering a dreadful miss for Birmingham as he skyed the ball way into the stands after running onto a Jermaine Pennant cross.
And a minute later, team-mate Morrison twice hit the crossbar in the space of just 60 seconds.
To rapturous applause at Carrow Road, however, Norwich just held on.
Birmingham boss Steve Bruce:
"I can't defend anybody who raises a punch or a slap or whatever it was [Damien Johnson].
"We all know the rules so I can't defend him. And you do something like that and it costs your team.
"The better team lost today. I'm convinced with 11 men we would have won today.
"All the Norwich fans will go away thinking 'we have been extremely lucky today'."
Norwich: Green, Helveg, Fleming, Shackell, Drury (Charlton 72), Bentley, Safri (Holt 63), Francis, Huckerby, McKenzie (Svensson 86), Ashton.
Subs Not Used: Jonson, Lewis.
Goals: Ashton 45 pen.
Birmingham: Maik Taylor, Melchiot, Cunningham (Blake 78), Upson, Clapham, Pennant, Johnson, Nafti, Lazaridis (Clemence 19), Heskey, Pandiani (Morrison 45).
Subs Not Used: Martin Taylor, Vaesen.
Sent Off: Johnson (31).
Booked: Nafti, Cunningham, Morrison, Pennant, Clemence.
Ref: S Bennett (Kent).