David Healy had the chance to mark his return to Norwich on a second loan spell with an early goal, but his close-range effort cleared the bar after Clint Easton created the chance by heading down Steen Nedergaard's right-wing cross in the ninth minute.
On the half hour Zema Abbey missed a gilt-edged chance when he headed over from close range after Nedergaard had set him up with an inch-perfect cross.
Nedergaard then put Norwich ahead with a stunning right-foot drive from more than 30 yards which eluded the Coventry keeper's despairing dive to his right.
A snap shot from Healy was too close to the keeper to trouble him and he was then booked for a late tackle on Andrew Whing five minutes before half time.
Norwich forced three corners in the opening minutes of the second half before Youssef Safri replaced Richie Partridge in the 52nd minute.
Calum Davenport denied Healy a shooting chance with a well-timed interception.
Whing made way for Craig Pead after 58 minutes and Coventry enjoyed a spell of pressure, then Mark Rivers was put through by Healy but fired over with only the keeper to beat.
Gary McAllister produced the visitors' best effort in the 65th minute but Robert Green did well to tip his shot over.
Green made an even better save to keep out Davenport's header from McAllister's free-kick.
Darel Russell wasted the chance to make the point safe when he fired wide with only the keeper to beat.
Paul McVeigh came on for Healy and set up the second goal in the last minute for Adam Drury to fire in from close range.