Matt Taylor’s League One side threatened an upset when Luke McCormick fired them ahead after 20 minutes but Norwich rallied in the second half with goals from Gabriel Sara, Adam Idah and Kenny McLean seeing them into round four.
Rovers began the third-round replay brightly and former Norwich striker Chris Martin saw an early effort drift just wide before Luke Thomas’ header was comfortably saved by George Long.
Norwich, without the injured Josh Sargent, struggled to get going as an attacking force and that allowed the Gas to continue to press with only a superb Long save denying Antony Evans.
It proved to be only temporary respite for Norwich as from the subsequent corner McCormick put the Gas in command with a carefully-placed low drive from just inside the penalty area.
Things went from bad to worse for Wagner’s lacklustre side when defender Danny Batth limped off injured.
Norwich were sparked into life by the energetic Sara, who finally gave the travelling supporters something to shout about with a long-range effort that Matt Cox did well to push over.
Rovers continued to enjoy the upper hand after the break and only a fine, low save by Long kept out Thomas’ powerfully-struck shot and only desperate defending kept the hosts at bay as they pressed for a potentially decisive second goal.
Norwich got their attacking act together and were level on 53 minutes thanks to the impressive Sara, who bundled the ball home from close range after Sam McCallum’s effort struck the post with the Rovers defence at sixes and sevens.
Rovers were soon back on the front foot but were punished for their ambition when they were caught out on a swift counter-attack by the marauding Canaries.
The hosts were left outnumbered as Norwich poured forward and were punished when Connor Taylor brought down McLean in the box following a collision.
