The Canaries followed up their 4-0 drubbing of Leyton Orient on Tuesday with an equally emphatic win with Jame Cureton's injury-time goal adding to first-half strikes from Chris Martin, Wesley Hoolahan and a brace from Grant Holt.
The Canaries were on the front foot from the moment Martin curled home a free-kick from the edge of the area on eight minutes, although Rovers did manage to get on level terms when Jeff Hughes converted from the spot after a foul on Jo Kuffour.
Norwich restored their advantage on the half-hour mark via another soft penalty, with Hoolahan sending keeper Mikkel Andersen the wrong way after Byron Anthony had tussled with Hoolahan in the area.
Three minutes later it was 3-1 as Grant Holt took advantage of some dreadful defending and Norwich's top scorer soon made it nine for the season when he ran through virtually unchallenged before producing a clinical finish to make it four at half-time.
The hosts had the final word when substitute Jamie Cureton lashed home in injury time after more good work by Hoolahan to make it a thoroughly miserable afternoon for his former club.