The Blades had looked on the right track to claim a hugely credible draw against the reigning Premier League champions, with Dean Henderson saving a Gabriel Jesus penalty within the half as well as creating a string of wonderful saves.
But Aguero came off the bench to attain the decisive goal, tapping in a cross from Kevin de Bruyne towards the end of the half.
That strike came just moments when Sheffield United came close to taking the lead themselves – Oli McBurnie stretching to meet a cross however just failing to turn the ball into an empty net.
Victory for Manchester city means that they strengthen their place in second. they have fifty one points – thirteen behind leaders Liverpool however six ahead of Leicester, who play West Ham on Wednesday.
Sheffield United, meanwhile, stay seventh on thirty three points.