The scoreline barely reflected the hosts' dominance as they comfortably recorded their first clean sheet of the season in a one-sided contest at the Etihad Stadium.
There may have been some nerves with only Kolarov's fifth-minute free-kick to show for their first-half efforts, but the Black Cats were then overrun as they slipped to their first loss of the season. Aguero came off the bench to add the second on the hour and Milner fired a free-kick through Simon Mignolet after 89 minutes.
Just as pleasing for City will have been their defensive solidity, which they rediscovered without their backline linchpin and captain Vincent Kompany, who was ruled out with a calf injury.
Micah Richards made a surprise return from an ankle injury in his place while Joleon Lescott was also restored to the defence. Yaya Toure took over as skipper, playing alongside Gareth Barry in midfield, while Carlos Tevez and Mario Balotelli started up front.
City took the lead after Tevez was crudely brought down by Carlos Cuellar on their first attack.
The Argentinian had broken clear but was felled by a late tackle on the edge of the box and referee Lee Probert brandished the yellow card.
The City supporters felt it should have been red but they did not complain for long as Kolarov stepped up to curl a superb free-kick past Mignolet at the near post.
The second goal finally came as Aguero raced to the near post to turn in a vicious Kolarov ball from six yards.
Yet they would not settle for two and Milner whipped in a free-kick from the left of the box which took a slight deflection off the head of Craig Gardner to evade Mignolet's grasp.
Source: PA
Source: PA