Brett Emerton fired in his first of the season, before Paul Dickov and Lucas Neill secured the win for the home side against ten-man Leeds.
Mark Hughes made two changes to the side which defeated Birmingham at the weekend, Andy Todd replacing Ryan Nelsen, while Emerton came in for David Bentley on the right.
With a mixture of injuries and suspensions to contend with, Kevin Blackwell made five changes to his Leeds side that held Sheffield United to a 1-1 draw on Friday.
Both sides started brightly with the ball fizzing across the wet surface, but it was Rovers who registered the first notable effort on goal. On 12 minutes, Shefki Kuqi danced past four Leeds players before firing narrowly wide of the post.
Eight minutes later and the big Finn was involved again. After good work by Neill, Robbie Savage and Dickov, Kuqi found himself with time and space to cross and after picking out the unmarked Emerton on the edge of the box, the Aussie ought to have done better with the finish.
Rovers continued to create the better chances and Dickov's first-time shot warmed Neil Sullivan's gloves on 32 minutes. After a delightful Tugay cross with the outside of his boot, Kuqi flashed a header wide of goal and that proved to be his final involvement in the game, as on 53 minutes he was replaced by Bellamy.
The substitution worked wonders for Hughes, as just seven minutes later Rovers hit the front. After some midfield magic from Tugay, Bellamy played the perfect through ball for Emerton and the Aussie winger drove the ball home inside Sullivan's near post.
Blackwell rang the changes, with American international Eddie Lewis and on-loan Rovers midfielder Jonathon Douglas coming on, but it was Rovers who grabbed the all important second goal.
Bellamy galloped fully 60 yards down the left touchline before providing the perfect ball for Dickov, who had the simple task of finding an open goal from six yards.
And after Gylfi Einarsson was shown a straight red for a tackle on Savage, Neill completed the scoring, latching on to Bellamy's superb pass.