The defending champions maintained their recent supremacy over their fiercest rivals by winning 1-0 at Etihad Stadium, with Aguero finishing off a sweeping move in the 63rd. City now has four straight league victories against United for the first time since the 1969-70 season.
United couldn't hold out after defender Chris Smalling was sent off in the 39th minute for two quick yellow cards and now has just 13 points from 10 matches — its lowest haul since 1986, when Ron Atkinson was fired and replaced by Alex Ferguson.
United manager Louis van Gaal spent $250 million over the summer to rebuild the team after last season's dismal season under David Moyes but is finding results just as hard to come by.
Chelsea has twice as many points as ninth-placed United after more than a quarter of the campaign.
Tottenham also benefited from a red card in Sunday's other game, scoring two goals in the final six minutes of normal time through Nacer Chadli and Harry Kane to beat 10-man Aston Villa 2-1.
Christian Benteke was sent off for pushing in the 65th, checking Villa's momentum after Andreas Weimann's first-half opener. Villa has now lost six straight games, a run that is piling the pressure on manager Paul Lambert.
After spending so long in the shadow of United in Ferguson's trophy-filled tenure, the blue half of Manchester is basking in a period of dominance not seen in 44 years.
This latest win kept City six points behind Chelsea but it was hardly convincing, despite playing against 10 men for more than half the game.
Booked needlessly in the 31st for impeding an out-of-hand clearance by goalkeeper Joe Hart, Smalling dived into a challenge on James Milner eight minutes later and was shown a second yellow card that Van Gaal labeled "stupid."
It got worse for United when Smalling's centre-back partner, Marcos Rojo, was carried off on a stretcher in the 55th minute with a dislocated left shoulder. The visitors' makeshift defence now consisted of two midfielders in Antonio Valencia and substitute Michael Carrick and two 19-year-olds.
When Aguero turned home a cross from Gael Clichy to score his league-high 10th goal of the season, it looked like City would go on to win easily, but United finished the game stronger and had chances to equalize through Angel Di Maria and Marouane Fellaini.
"I have seen willpower of this team that I said to the players is fantastic," Van Gaal said, "but we have still only 13 points out of 10 games and that is not so much."
Van Gaal played down suggestions that Fellaini spat at Aguero as he stood over the striker following a first-half challenge.
"I heard that it is a question on social media but that it has showed he is shouting," Van Gaal said. "Sometimes when you shout, there is a little bit of saliva so I don't think he is a spitting figure."