A turgid beginning by both sides was punctuated by flashes of skill from Elano and Robinho, a sign of things to come, including a sumptuous early dummy by Robinho that left his marker wrong-footed.
Fortunately, City began to get more penetration in the second quarter of the game and the scoring was opened by Felipe Caicedo's goal for City.
It was a scrappy affair - scrambled over the line from six yards out by the Ecuadorian striker after Nigel de Jong and Nedum Onuoha had controlled the ball following Elano's corner.
With the lead safely in their possession, City took control of the rest of the first half.
Robinho had been showing off his skills throughout the game and he deservedly put City 2-0 ahead with a 20-yard drive after Vincent Kompany's lay-off following the Belgian's interception of Andre Ooijer's clearance on the edge of the Rovers box.
The visitors were looking short of ideas, especially after an early knock to striker Benni McCarthy, who was replaced at half-time.
The South African provided their closest first-half chance on goal - a header from El Hadji Diouf's cross that grazed the top of Shay Given's goal - but City effectively sealed the three points with a third goal before the break.
Stephen Ireland's attempt to cross the ball was handled by Gael Givet in first-half stoppage time.
Rovers captain Ryan Nelsen, Vince Grella and Ooijer were all booked for dissent following the penalty call and Elano capped a fine first-half display by sending Paul Robinson the wrong way to make it 3-0 at the break.
Rovers improved in the second half and had a glimmer of hope when Onuoha conceded a penalty in the 66th minute after he tripped Morten Gamst Pedersen.
Substitute Keith Andrews pulled one back for Rovers after Given's brilliant double save from Diouf's penalty fell to him at an acute angle. It was hard luck for the Irish keeper but Blackburn never looked in danger of getting anything out of the game.