United were reduced to 10 men late on in the first half when Chris Smalling was sent off for two bookable offences in the space of eight minutes.
After seeing three penalty claims turned down Aguero grabbed the crucial breakthrough for Manchester City just past the hour mark with a fine finish
United threw everything at City in the closing stages with Angel 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.
After a fast and frenetic start City created the first chance of the game on eight minutes when Aguero picked up a pass from James Milner and cut inside Antonio Valencia before firing in a shot which was punched away by David De Gea.
Two minutes later United had an opening when Robin van Persie headed the ball down into the path of Adnan Januzaj on the edge of the box, but the midfielder dragged his shot wide of the target.
Aguero looked like he was in the mood to score and he fashioned an opportunity for himself on 20 minutes when he brilliantly brought down Fernando’s pass upfield, but after being pushed wide by Marcos Rojo he failed to get enough power on his shot to trouble De Gea.
De Gea came to United’s rescue twice in the space of a minute with two superb saves to deny Jesus Navas and Aguero.
Aguero created the first chance for Navas when he spotted his run into the box, but the winger saw his shot kept out by De Gea and seconds later the United goalkeeper bravely denied Aguero from close-range after Fernando had picked out the Argentine striker inside the box with a brilliant cross from the left.
Smalling picked up his first booking on 31 minutes for needlessly charging down a Joe Hart kick as he tried to set City away on the counter attack.
The United defender was made to pay for that silly booking eight minutes later when he was shown a second yellow card for a late challenge on James Milner leaving the visitors to play 50 minutes with just 10 men.
City had strong claims for a penalty rejected three minutes before the break when Marouane Fellaini, who was filling in at centre-half following Smalling’s dismissal, appeared to bring down Aguero inside the box, but referee Michael Oliver waved away their appeals.
Louis van Gaal decided to shuffle his pack soon after when he brought on Michael Carrick for Januzaj to help fill the void left by Smalling’s early exit.
City poured forward in search of a goal and they felt they should have won a penalty right on the stroke of half-time when Yaya Toure appeared to be caught by Rojo’s outstretched leg as the Ivorian tried to get on the end of Stevan Jovetic’s chipped pass.
As expected, it was one-way traffic at the start of the second half and United suffered another defensive blow on 53 minutes when Rojo was forced off with an apparent shoulder problem with youngster Paddy McNair coming on in his place to leave the visitors with a real makeshift back four of Carrick, McNair, Valencia and Luke Shaw.
City had strong claims for a penalty – their third of the game – on the hour mark when Aguero weaved his way into the box before appearing to be clipped by Carrick, but again referee Oliver ignored the home side’s appeals.
Two minutes later 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.
A minute later Fellaini wasted a great opening when he lost his marker Vincent Kompany to get on the end of Di Maria’s free-kick, but he got his header all wrong with his effort coming off his shoulder and well wide of the target.
Toure went close to easing City’s nerves in the final minute when he skilfully turned McNair on the edge of the box and curled his shot just wide of the target, but it did not matter as City held on to take all three points and close the gap on leaders Chelsea to six points.