The Blades went the closest to breaking the deadlock in a goalless first half. Lys Mousset ran through and fired a low shot past Claudio Bravo but saw his effort ruled out for a marginal offside by VAR.
Aguero blasted the opener past goalkeeper Dean Henderson on 52 minutes after being sent through on goal by a pinpoint pass from De Bruyne.
The Belgium international then wrapped up the win on 82 minutes, curling a low strike past Henderson after a good run from Riyad Mahrez.
Manchester City were without suspended goalkeeper Ederson for Sunday's clash, meaning Bravo started in goal with Eric Garcia and Oleksandr Zinchenko also coming into the starting XI.
The visitors also made three changes to their team. Mousset and Callum Robinson were drafted into the attack, while Muhamed Besic replaced the injured John Lundstram.
The Athletic's Sam Lee shared the two teams:
Both sides had sights of goal in an evenly contested first half. De Bruyne and Zinchenko both blazed shots over the bar for the hosts, while Mahrez saw an effort blocked by John Egan.
Mousset sent an early header wide of target for the Blades but did get the ball in the back of the net on 29 minutes. However, the goal was not allowed to stand as the 23-year-old was ruled to be just offside in the build-up:
Manchester City took the lead early in the second half through Aguero. De Bruyne was quick to latch on to a loose ball and produced a slide-rule pass for Aguero to power past Henderson:
32 - Sheffield United have become the 32nd different opponent that Sergio Aguero has scored against in the @premierleague out of the 33 he has faced (97%); only against Bolton (one app, no goals) has he failed to find the net in the competition. Collection. #MCISHU https://t.co/Nzo8lgx9kr
The goal was met by angry protests from Sheffield United, who felt the referee had obstructed John Fleck in the build-up:
Manchester City appealed for a penalty on 70 minutes when Mahrez cut inside and saw a shot that appeared to come off Egan's arm, but it was deemed to be accidental.
The hosts had to wait until deep into the second half to make the game safe. A surging run from Mahrez saw the winger release De Bruyne, who nudged the ball on to his right foot and swept a powerful effort home:
The visitors almost pulled one back in stoppage time. Substitute Billy Sharp headed Enda Stevens' cross on to the post and saw it trickle along the goalline and away to safety.
Sheffield United forced Pep Guardiola's side to work hard for their win, but the defending champions were good value for the three points and close to within a point of Leicester City in second place.