Norwich progress to the third round of the Carling Cup courtesy of a 25 yard strike from Youssef Safri, his first goal for his new club.
The home side kicked off attacking the Barcley end goal with Rovers packing the mid field and leaving Junior Agogo as a lone front runner.
Paul McVeigh, in for David Bentley, mis-cued twice to relieve early pressure on the visitors.
Agogo had a shot blocked then Gary Doherty failed to beat Kevin Miller in a one-on-one situation. The keeper stood up well but the City striker shot straight at him.
Darren Huckerby delivered a low cross from the right but no Norwich player could get on the end of it.
In the 18th minute McVeigh crossed from the right but Doherty headed wide of the near post.
After soaking up the pressure Rovers became a little more adventurous and Agogo fired over in the 25th minute with a rasping drive.
Huckerby's chipped pass was gathered by Miller before it reached Damien Francis.
Adam Drury had the ball in the net after 34 minutes but the goal was disallowed, referee Kevin Friend, penalising Doherty.
Green saved from Steve Elliott and Stuart Campbell. A shot from Agogo was deflected for a corner by Craig Fleming.
When it looked as if Rovers had done enough to go in at half time with the scores level at 0-0, Youssef Safri collected a pass from Thomas Helveg and beat Miller to his right with a low right-foot shot from a good 25 yards.
Huckerby fired into the side netting 2 minutes into the second half, after a determined run into the area by Adam Drury.
The Premiership side found it difficult to find a way through the Rovers defence. When McVeigh beat the keeper with a header from Huckerby's cross, Ali Gibb headed off the line.
Substitute Craig Disley missed Rovers best chance of an equaliser when he fired wide from close range.
In the last minute of the game Elliott received a second yellow card for tripping Huckerby but the referee told Rovers Manager, Ian Atkins, that he would look at the decision again and might reconsider the second booking.