United looked to have grabbed the lead through Lys Mousett in the 28th minute but the goal was ruled out after a VAR review found the slimmest of margins of offside.
Moments after the incident, both sets of supporters expressed their opposition to the VAR system in a loud, united chant.
Third-placed City, beaten by Wolverhampton Wanderers on Friday and now still 14 points behind leaders Liverpool, finally took the lead in the 52nd minute through Aguero, who blasted home after being slipped in by De Bruyne.
Sheffield United players argued furiously that during the build-up the ball had struck referee Chris Kavanagh and a drop ball should have been called, but after a brief review the goal stood.
City wrapped up the win which leaves them just a point behind second-placed Leicester City, in the 82nd minute, when De Bruyne drove home at the end of a swift counter-attack from Riyad Mahrez. (Reuters)