But the Canaries' real hero was former Coventry striker Darren Huckerby, as his pace terrorised his old club and he had a hand in both goals.
The Sky Blues had their chances as they dominated for long spells but they always looked in danger when Norwich hit them on the break.
Coventry began brightly and could have gone ahead inside the opening ten minutes when Steve Staunton's effort from six yards was deflected over the bar and Eric Deloumeaux's shot was turned wide by Robert Green.
Huckerby came into the game midway through the half - doing most of his work on the left as teenage right-back Andrew Whing struggled to cope with his speed.
The striker almost opened the scoring on the half-hour mark but his snapshot from the edge of the area was just wide.
But he turned provider in the 37th minute when he breezed past Whing and crossed to the far post. Damien Francis volleyed the ball goalwards and Holt helped the ball over the line from two yards.
Scott Shearer made a smart save from Iwan Roberts who could have killed the game before half-time when he broke free from Huckerby's pass.
Coventry continued to enjoy territorial advantage in the second half and they finally began to turn their possession into chances.
Patrick Suffo hit a couple of efforts just wide before Craig Pead headed Michael Doyle's cross just over the top.
Doyle, Mo Konjic and Graham Barrett all spurned chances to put the home side level before the league leaders finally made the game safe with five minutes to go.
Huckerby cut into the box again and laid the ball on a plate for Brennan, who cracked a shot from the edge of the area which flew past Shearer and into the top corner.
Julian Joachim, who had a quiet game for the Sky Blues, could have reduced the arrears late on, but Green did well to hold on to his low shot from just inside the box.