United manager Van Gaal’s side had to play more than half the match a man down as defender Chris Smalling was sent off in the 39th minute after collecting two needless yellow cards, having charged down goalkeeper Joe Hart’s clearance kick before a reckless foul on James Milner.
City had several penalty appeals rejected by referee Michael Oliver before Aguero fired City into a 63rd-minute lead after finishing from close range to crown a superb one-touch move involving Yaya Toure and Gael Clichy.
The Argentinian striker’s 10th league goal of the season left him top of the Premier League scoring charts after he had been tied on nine goals with Chelsea’s Diego Costa heading into this weekend’s round of matches.
Hart then saved well from Angel di Maria to deny United an equaliser 14 minutes from time before Marouane Fellaini wastefully headed wide when well-placed to make it 1-1.
Toure, however, could have made it 2-0 in the first of five minutes of added-on time but headed over the top from close range.
Victory saw Premier League champions City move to within six points of leaders Chelsea but still remain third, two points adrift of second-placed Southampton.
United’s third league loss of the season meant they dropped to ninth on goals scored and remained 13 points off the summit.