Leicester moved up to third as the Foxes unbeaten start to the season continued in a 3-1 win over Bournemouth, while victories for Crystal Palace and West Ham take them into a share of fourth.
City win comes at a cost
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Liverpool can move back above City should they continue the only 100 percent start left in the Premier League later at Burnley, but City were never in danger of dropping points at the Etihad as Kevin de Bruyne tapped home David Silva's cut-back after just two minutes.
Victory came at a cost for Pep Guardiola's men as Aymeric Laporte was stretchered off with a knee injury that looks certain to rule him out of winning a first cap for France in upcoming Euro 2020 qualifiers.
"He has gone to the hospital. Tomorrow we will know exactly what he has. I think he will be out for a while," said City manager Pep Guardiola on Laporte's injury.
Aguero soon made the game safe by blasting high into the net just before the break and produced another sublime finish to curl into the top corner for his second 10 minutes into the second-half.
Substitute Bernardo Silva then rounded off the scoring for the champions.
"I love to see opposite teams play that way - that have that courage," added Guardiola. "They had chances to score as well but we were clinical."
United slump continues
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How United must wish they had some of their local rivals firepower as Southampton clung on for a 1-1 draw at St. Mary's despite playing the last 17 minutes plus stoppage time a man down after Kevin Danso's red card.
Daniel James had given the visitors the perfect start with his third goal in four appearances for United, but Jannik Vestergaard headed home an equaliser just before the hour mark.
Ole Gunnar Solskjaer's men have now failed to win in their last three games and won just one of their last 10 dating back to last season.
"We've been dominating, creating chances and just haven't been clinical in front of goal to win the games," said Solskjaer.
"It's not a dip in form, (but) it's a dip in results definitely."
Blades blunt Chelsea
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After scoring his first Chelsea goals away to Norwich last weekend, Tammy Abraham thought he had given the Blues all three points at home to newly-promoted Sheffield United by scoring twice more before the break.
However, the Blades hit back at the start of the second-half through Callum Robinson and Kurt Zouma's own goal a minute from time earned the visitors an unlikely point in a 2-2 draw.
"We have to take responsibility, we allowed that to happen. It was on us to take the game away from them and we allowed them to get back into it," said Chelsea boss Frank Lampard, who is still waiting to win his first match in charge at Stamford Bridge.
"If we can't go on and get a third goal that's something we have to work on, this is the Premier League, it's ruthless."
As United and Chelsea stumble, Leicester are the closest challengers to the top two, but Brendan Rodgers's men were also lucky Youri Tielemans did not see red in another controversial VAR call.
The Belgian should have been sent-off for a high challenge on Callum Wilson with Leicester leading 2-1 early in the second-half, but, after a VAR review, the original decision to let Tielemans escape unpunished stood before Jamie Vardy secured the points with his second goal of the game.
"He missed the ball and went over the top and went on to my ankle. If it's not clear and obvious then I don't know what is," said an angry Wilson.
Crystal Palace backed up their shock victory at Old Trafford last weekend with a 1-0 win over 10-man Aston Villa thanks to Jordan Ayew's goal 17 minutes from time.
West Ham also have seven points from four games as goals either side of half-time from Sebastien Haller and Andriy Yarmolenko secured a comfortable 2-0 over Norwich.
Watford got their first point of the season, but remain bottom after a 1-1 draw at Newcastle.