City have now won their last 18 Premier League games at home, dating back more than a year, and equal Newcastle's record of starting a season by winning each of their 13 home matches.
Balotelli put Roberto Mancini's side in front with his ninth Premier League goal of the season with just under half an hour gone.
Aguero added a second with his 16th - and 21st in all competitions - just after half-time.
Dzeko came off the bench to head a third as City coasted to a comfortable victory that moves them five points ahead of United, who have an away game at Norwich on Sunday.
The result left Blackburn firmly rooted in the relegation zone, where only two points separate the bottom five.
Balotelli was making his first Premier League start since the goalless draw at West Brom in December following a four-match ban.
But he took just a minute to cause Blackburn problems, latching on to an Adam Johnson cross and forcing an impressive low save from Rovers goalkeeper Paul Robinson.
Rovers went into the game having lost just half of their 12 away matches and soon produced a threat of their own when a Morten Gamst Pedersen free-kick fell for Grant Hanley and his close-range effort deflected wide off Joleon Lescott.
The visitors were pinned back deep into their own half and were grateful to goalkeeper Robinson for keeping them in the game.
When Aguero swung a pass over to right flank, Johnson burst forward and had a long-range strike pushed away by the former England goalkeeper and Robinson also got a hand to the Pablo Zabaleta cross that followed.
As City continued to probe, Balotelli had a bending free-kick pushed away by the Rovers goalkeeper.
But just before the half hour Balotelli made the breakthrough in some style.
Making his first Premier League appearance since returning from African Nations Cup duty with Ivory Coast, Yaya Toure started a counter-attack with a clever pass to David Silva.
The Spaniard clipped the ball left for Aleksander Kolarov, who whipped in a cross that gave Balotelli an easy tap in at the near post.
The Italy striker displayed a "Raffaella ti amo (Raffaella I Love You)" t-shirt, aimed at girlfriend Raffaella Fico as he celebrated his opening effort.
City continued to press for a second goal, and Robinson had to be at his best to deny Silva, who was played through by another intelligent pass from Kolarov.
Robinson pulled off another fine stop from a Vincent Kompany flick from Kolarov's corner before Toure failed to divert the rebound on target.
Argentina forward Aguero also failed to take two opportunities just before the break, lifting well over the bar and also missing from a narrow angle.
The pattern continued after the break, with Johnson having a low effort deflected wide of goal.
But from the Silva corner that followed, Robinson flailed at the ball and Aguero stabbed in City's second.
Even Zabaleta was attempting to score and the Argentina defender saw his effort fly sideways straight into Aguero and wide of goal.
As Blackburn attempted some sort of response, Canadian winger Junior Hoilett broke forward and shot only to see his effort bounce away off Yakubu.
Balotelli had a header deflected off-target by Bradley Orr but City seemed satisfied with their margin of victory.
With just under 10 minutes left, Dzeko beat two Blackburn defenders to thump Kolarov's cross past Robinson.
Yakubu finally forced a save from Joe Hart deep in injury time but it was a comfortable outing for the leaders.