Goals at the end of each half saw Rovers record their second successive Premier League 2 victory.
The home side were slow starters at Ewood Park as Norwich impressed early on, but after the lively Elliott Bennett had struck the bar, Connor Mahoney teed up Lewis Mansell to head Rovers in front just before the break.
There were fewer chances in the second half, but Damien Johnson's side struck the decisive blow four minutes from time when Mahoney converted from the spot after substitute Connor Thomson had been tripped.
Ahead of the game Rovers were able to call upon the experienced pair of Elliott Bennett and Adam Henley who were given the opportunity to step up their fitness after recovering from hamstring strains picked up in the first week of the season. Whilst trialist Wes Brown was also named amongst the starters.
Yet it was the visitors, who went into the match off the back of three straight league defeats, who gave Rovers the runaround in the opening exchanges.
Just two minutes in and Norwich broke quickly from a Rovers free-kick, but Glenn Middleton fired just wide with a shot across the box. However, in giving chase Henley immediately pulled up, meaning his return to match action would be short-lived. Ryan Nyambe came on in his place.
The Canaries continued to look for the opener and only an important tackle from captain Matty Platt prevented Benny Ashley-Seal from getting his shot away inside the box. The resulting corner saw Andy Fisher called upon to make a fine save, tipping over Joe Crowe's header at the back post.
With the Canaries quicker to the ball and stronger in the tackle, Rovers struggled to get out of their own half in a one-sided opening period. On 12 minutes Ebou Adams beat the offside trap to square for Ashley-Seal but the forward lost his footing just as he was shooting.
But as the half wore on the home side finally managed to gain a foothold in the game, with Bennett at the heart of everything that was good for the side in blue and white.
The former Norwich man first forced a fingertip save from Ben Killip, before going even closer when he smashed an effort against the crossbar following Nyambe's cut-back.
Bennett and Mahoney then combined to find Lewis Hardcastle racing down the right, but as the midfielder curled a ball to the back post, a sliding Mansell just couldn't connect.
Two minutes before half-time Rovers grabbed the opening goal their improved play had threatened. Bennett found Mahoney racing into the area, and, after teasing his marker, he stood the ball up to the back post for Mansell who had time and space to head home from six yards for his second goal this season.
The home side could have doubled their advantage in added time at the end of the half. Killip, who once played for Rovers as a trialist, saving well to keep out a well-struck shot from Mahoney.
In contrast, the second half was a much tighter affair with less goalmouth opportunities than the opening 45.
Bennett saw an early effort saved after good work from Jack Doyle, whilst Ebou Adams' shot deflected just wide at the other end.
Further half-chances followed for Mahoney for Rovers and Middleton for Norwich, but neither goal was meaningfully threatened.
With 14 minutes to go Bennett made way to warm applause from the Rovers fans. The midfielder had impressed on his return to match action.
His replacement Connor Thomson would play his part in ensuring all three points would go Rovers' way. Breaking into the box four minutes from time the midfielder was tripped by Michee Efete and Mahoney made no mistake from 12-yards to wrap up the victory.
ROVERS: Fisher, Henley (sub Nyambe 3 mins), Doyle, Travis, Platt (c), Brown, Mahoney, Rankin-Costello (sub Thomson 64 mins), Mansell, Hardcastle, Bennett (sub Grayson 76 mins).
Subs not used: Ascroft (GK), Magloire.
Goals: Mansell 43 mins, Mahoney (pen) 86 mins.
Booked: Brown 48 mins, Travis 45+3 mins.
NORWICH: Killip (c), Efete, Ramsey, Mutataia-Sambu, Godfrey, Crowe (sub Higgs 82 mins), Jaiyesimi, Grant, Ashley-Seal, Adams (sub McIntosh 79 mins), Middleton.
Subs not used: Hallett (GK), Wallis, Odusina.
Booked: Crowe 19 mins, Efete 86 mins.