Anthony Martial pulled a goal back from the penalty spot shortly before the hour mark, but Ilkay Gundogan came off the bench to secure the points for City as they extended their unbeaten start to the campaign to 12 matches.
City had dropped down the table as a result of Liverpool's win over Fulham earlier in the day, but they quickly set about restoring their place at the top of the standings as United made another slow start to the match.
The home side enjoyed 87% of possession in the opening 10 minutes and almost broke the deadlock on a few occasions early on, with both Bernardo Silva and Fernandinho missing the target from range and Aguero missing the ball entirely when well placed inside the area.
There was an air of inevitability when the first goal did arrive after only 12 minutes, with Raheem Sterling's dangerous delivery being knocked back across goal by Bernardo for David Silva, who kept his composure before firing a deflected effort past David de Gea.
It was the seventh time in 12 Premier League games this season that United have conceded the first goal, and City initially looked more than capable of adding to their advantage sooner rather than later.
However, United did begin to settle into the game and created their best opening of the first half after 26 minutes when Chris Smalling sent a looping header onto the roof of the net.
City continued to enjoy the lion's share of possession, but they struggled to translate that into chances and were limited to a long-range Aymeric Laporte shot and an Aguero half-chance from a tight angle for the remainder of the half.
Indeed, Silva's goal proved to be the only shot on target either side managed in the opening 45 minutes, but that changed soon after the restart as City made another quick start to double their advantage.
Aguero exchanged passes with Bernardo inside the penalty area before blasting his finish through the hands of De Gea and into the roof of the net for his eighth Premier League goal of the season.
The home side could have put the game to bed shortly afterwards when Fernandinho's pass released Sterling inside the box, but the in-form winger took too long over his finish and was eventually crowded out by three United defenders.
Manager Jose Mourinho brought on Romelu Lukaku in an attempt to get back into the game, and the fit-again striker made an impact within 30 seconds of his introduction when he won a penalty after Ederson had rashly come for the ball but only succeeded in bringing Lukaku down.
Martial stepped up to take the spot kick and sent Ederson the wrong way to become just the seventh Manchester United player and the fifth French player to score in five consecutive Premier League appearances.
City were not fazed by United's goal back, though, and quickly reassumed control of possession with Fernandinho and Leroy Sane threatening to restore their two-goal advantage.
Guardiola replaced Aguero for Gundogan with less than 15 minutes remaining, and the German skewed one effort well off target before making sure of the points by adding City's third four minutes from time.
Gundogan was left unmarked inside the area at the end of a lengthy passing move and had the time to take a touch before sweeping his finish past De Gea.
There was no way back for United this time as they failed to build on their famous victory in Turin on Wednesday night, falling to a defeat which leaves them already 12 points adrift of City after only 12 games of the season.
United have also now conceded 21 goals in the league this season - their highest tally after 12 games of a top-flight campaign since 1966.
MAN CITY (4-3-3): Ederson; Walker, Stones, Laporte, Mendy; Bernardo, Fernandinho, Silva (Foden 92'); Mahrez (Sane 62'), Aguero (Gundogan 75'), Sterling
MAN UTD (4-3-3): De Gea; Young, Smalling, Lindelof, Shaw; Herrera (Mata 73'), Fellaini, Matic; Lingard (Lukaku 57'), Rashford (Sanchez 73'), Martial
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