Holt, who missed last Saturday's home defeat to Portsmouth due to a one-match ban, opened the scoring in the 64th minute with a powerful diving header from Russell Martin's cross for his 10th goal of the season.
It was also the first goal Coventry had conceded in 460 minutes.
But the home side, reduced to 10 men in the 35th minute when Aron Gunnarsson was dismissed for a two-footed lunge on on-loan Norwich midfielder Henri Lansbury, levelled nine minutes later.
Striker Marlon King broke away from the visiting defence to fire past goalkeeper John Ruddy for his second goal in three games.
However, Holt earned the Canaries a fifth away win of the season when he pounced from 12 yards with three minutes remaining.
There was still time for Coventry substitute Freddy Eastwood, who had only been on the pitch for a couple of minutes, to hit the post.
The Canaries, who had won at Coventry only three times in 52 visits in all competitions, made an encouraging start and Chris Martin saw his 20-yard effort saved by goalkeeper Keiren Westwood.
Simeon Jackson then nearly caught out the Coventry defence but he lifted his 12-yard shot onto the roof of the net before Smith fired wide from 20 yards.
Coventry had to wait until the 29th minute for their first decent sight of goal, Gary McSheffrey putting his 18-yard wide.
Norwich responded and Lansbury, who has extended his loan spell from Arsenal until January 16, also failed to find the target from similar range.
Gunnarsson then saw red for a bad challenge on Lansbury.
Three minutes into the second half Holt, with nine goals this season, saw his header from Russell Martin's cross saved by Westwood and at the other end Martin Cranie, a half-time replacement for Bell for Coventry, had an effort collected by Ruddy.
Despite their numerical disadvantage, Coventry were holding firm and came close to taking the lead after 55 minutes but Richard Wood headed McSheffrey's corner wide from six yards.
Norwich, themselves, had two good opportunities from set-pieces of their own with Westwood superbly parrying a Holt shot from a David Fox corner and then Nelson heading wide.
But Holt was not to be denied again as he got away from his marker to head home Martin's cross to put Norwich ahead with 26 minutes left.
Coventry levelled nine minutes later when King escaped his marker to net for the second successive home game.
King and McSheffrey fired late chances wide for the home side while Westwood produced a fine save to tip Lansbury's 20-yard drive.
However, Holt won it for Norwich late on although Eastwood was denied by the woodwork for the battling hosts.