United were reduced to 10 men late on in the first half when Chris Smalling was sent off after two bookings in the space of eight minutes.
After seeing three penalty claims turned down, Aguero grabbed the crucial breakthrough for Manchester City. United threw everything at City in the closing stages with Di Maria seeing a shot superbly saved by Joe Hart and Marouane Fellaini wasting a good opening as the home side were forced to hang on against the 10 men of United.
City did make their numerical advantage count with Aguero breaking the deadlock with his 10th Premier League goal of the season.
Toure unlocked the United defence with a fine through-ball for Clichy down the left and he superbly pulled the ball back for Aguero to slam his left-footed shot high into the net past De Gea.
United went close to an equaliser on 70 minutes when out of nothing van Persie beat Martin Demichelis and Clichy down the left and fired in a shot which Hart kept out with his legs at his near post.
City were inches away from doubling their lead 15 minutes from time when Toure picked out Navas’ run into the box, but under pressure from Shaw he drilled his shot against the post.
Despite being down to ten men United almost grabbed a leveller on 77 minutes when Wayne Rooney burst through the middle and beat a couple of City defenders before going down in the box and the loose ball dropped to Di Maria who fired in a right-footed shot which was brilliantly saved by Hart low down to his right.
The win left the home side in third place with 20 points, six points behind Leaders Chelsea and United in ninth position with 13 points.