The Rovers boss made one change to the side that suffered a narrow defeat at Spurs last weekend, Morten Gamst Pedersen replacing Brett Emerton on the wing.
Olof Mellberg returned from suspension for the visitors, but David O'Leary was forced into a last-minute change after James Milner failed to shake off a virus during the warm-up and was replaced by Luke Moore in the starting line-up.
With less than 30 seconds on the clock, Villa should have been ahead following a long ball forward which was left by Rovers' centre-backs Todd and Ryan Nelsen, only for Gareth Barry to find himself clear on goal.
But after rounding man of the match Brad Friedel the 25-year-old midfielder fired wide of the open goal.
The visitors were on top and in a dominant three-minute spell midway through the first half they had three excellent opportunities to make the breakthrough.
Nelsen had to be at his very best to deny Kevin Phillips what looked like a certain goal, the unmarked Milan Baros then wasted a one-on-one with Friedel when he appeared to be offside, before the big American again came to the rescue, tipping over Mellberg's bullet header from a corner.
Following a lacklustre first-half display, Rovers came flying out of the traps after the break.
Three minutes in, Pedersen's in-swinging corner was headed goalwards by Bellamy and when Thomas Sorensen failed to hold on Todd was on hand to stab home the opener.
Ten minutes later and following a foul on Steven Reid, a training ground routine was put out for a corner and Rovers almost doubled their lead when Nelsen's towering header was cleared off the line by Moore.
Minutes later and again the visitors ought to have found the net.
On the hour mark, Friedel produced a brilliant reaction save to deny Baros and just two minutes later the Czech Republic star put a free header over the bar from seven yards out.
And O'Leary's men were made to pay when Rovers sealed victory 19 minutes from time. Florent Sinama Pongolle played in Pedersen and when the ball came back off Sorensen, Bellamy calmly slotted home his 13th goal of the campaign.