It was just City's second victory in their last seven fixtures in all competitions and their first cleansheet of the season at the 10th attempt. The win lifted Mancini's men into second place in the table, although Everton can climb back above them with a victory at Wigan later on Saturday.
City made the perfect start as Serbian defender Kolarov curled a superb fifth minute free-kick past Sunderland goalkeeper Simon Mignolet.
Sunderland were the only team to take a point off City at home in the Premier League last season, but they never looked likely to emulate that feat as their five-match unbeaten run came to an end.
Argentine substitute Aguero got the decisive second goal on the hour when he steered in a Kolarov cross from close-range for his first goal at Eastlands since the dramatic strike that won the title on the final day of last season.