Tyrhys Dolan scored with Rovers’ first shot as he blasted in at the near post and Sammie Szmodics doubled the lead soon after as fans at Carrow Road jeered a Norwich side that looked bereft of any confidence.
Wagner, who succeeded Dean Smith as Norwich boss in January when the Canaries were fifth, saw his afternoon get worse when Szmodics finished off a great move from close range soon after the break.
Rovers’ Scott Wharton was sent off a minute later for denying a goalscoring opportunity but City could not find a way back into the game until stoppage time when Gabriel Sara converted Przemyslaw Placheta’s cross.
Having been three points off top spot in September, Norwich have dropped to 17th place in the Championship table and earned just one point from their last six games, making it their worst start to a season in the second tier since they ended up being relegated to League One in 2008.
Meanwhile, Rovers’ fourth win in five league games moves them up to 10th, three points off the play-off places.
Dolan’s early goal – after lovely control from Joe Rankin-Costello’s pass to set himself up – shattered what little, fragile, confidence the Canaries had.
Soon after the lead was doubled as Andrew Moran’s pass picked out Szmodics, who peeled off debutant defender Jaden Warner and coolly side-footed into the bottom corner.
Norwich showed some attacking glimpses as Hwang Ui-jo looked dangerous at times, but they were poor in transition as Szmodics and Callum Brittain missed chances on the break.
