City's Brazilian striker Gabriel Jesus had a first-half penalty saved by Dean Henderson and the keeper, on loan from Manchester United, also produced a fine save to keep out a Raheem Sterling effort.
Aguero was sent on to replace Jesus in the 67th minute and it did not take long for him to make an impact as his perfectly-timed run into the box was picked out immaculately by Kevin De Bruyne, leaving the Argentine with a simple tap-in.
It was the sixth goal in three games for City's all-time top scorer and came moments after United had gone close to taking the lead with Oli McBurnie just unable to reach a low ball with his slide at the back post.
"Sergio is on fire right now. Strikers need momentum. It's good for us to have strikers in this form," said City manager Pep Guardiola.
"I am so happy with the team. I know what it's like to play here, it is a tough, tough place. We controlled it well and in the end we created chances to win," he said.
"It was an incredibly good victory for us to take a step towards securing Champions League football next season," added the Spaniard, whose side are on 51 points, 13 behind leaders Liverpool, who have two games in hand.
Laporte returns
City are six points ahead of third-placed Leicester City, who host West Ham United on Wednesday and 17 clear of fifth-placed local rivals Manchester United, who welcome Burnley.
Guardiola had defender Aymeric Laporte back in his lineup for the first time since he suffered a knee injury in August. The Frenchman was replaced 12 minutes from time.
"We knew that Aymeric couldn't play for 90 minutes, that's why we played five at the back to protect him a little bit. He's a crucial player for us, we've missed him, it's good for us to have him back," said Guardiola.
Sheffield United once again showed their quality with a determined and positive display and despite the loss the promoted side remain in seventh place on 33 points.
"Kevin de Bruyne has found an amazing pass and the movement of Sergio Aguero, he's done that to everyone in Europe and the world. It's a great finish. After that we're behind and it's double difficult for us," said United manager Chris Wilder.
"I've got nothing but an enormous amount of pride for my team. We went toe-to-toe with them. When opportunities arise you have to show a little bit of quality and we didn't do that sadly.
"Games are like this are what we're here for. We've worked really hard to get here, we want no regrets and I don't think there were tonight."
