Goals from James Milner and Gabriel Agbonlahor sealed the points for Martin O'Neill's men, who remain firmly in the hunt for a Champions League place.
But Rovers boss Sam Allardyce, who tasted defeat for the first time since taking charge at Ewood Park, had plenty of reasons to feel aggrieved after his team had a number of strong shouts for a penalty rejected by referee Steve Bennett.
Villa could have taken the lead after just three minutes when the lively Milner picked out Emile Heskey with a deep corner but the England striker planted his free header a yard wide of the far post.
The former Wigan striker did put the ball in the net minutes later from another set-piece but his effort was ruled out for a foul on Chris Samba.
However, Villa's large away following were soon cheering a legitimate opener as Milner broke the deadlock in stunning fashion in the 27th minute.
Picking the ball up following a short corner on the right, the former Newcastle man cut into the area before unleashing a venomous angled drive that snaked past Paul Robinson on its way into the far corner.
Milner went close to adding a second on the stroke of half-time but this time Robinson brilliantly diverted his scorching drive wide of the post.
In contrast, little was seen of Rovers as an attacking force in the opening 45 minutes, although they did have a strong case for a penalty turned down when Gareth Barry appeared to foul Benni McCarthy in the area.
Determined to inject more craft and guile, Allardyce brought on Tugay and new signing El Hadji Diouf at the beginning of the second half and the home side did improve as a result.
Rovers had a second penalty appeal turned down in the 73rd minute when Zat Knight tangled with Jason Roberts.
At the opposite end, Milner could have wrapped up the points but somehow the former Newcastle man dragged his shot wide from inside the six-yard box.
Substitute Roque Santa Cruz went close with a shot late on.
But Villa then grabbed a second in the final minute of normal time when Agbonlahor's shot took a deflection off Ryan Nelsen.