The Canaries recorded a comfortable win over their west Midlands opponents as striker Kyle Lafferty found the net on his first appearance for the club since January.
Strikes from Matt Jarvis, Kyle Lafferty and an own goal from Sebastien Pocognoli saw Norwich City progress to the fourth round of the League Cup at the expense of West Brom.
Norwich was the better side of the two at Carrow Road, but initially struggled to find an opening in the visitor's defense.
Gary O'Neil came close to breaking the deadlock in the first half, but was unfortunate to hit the post.