Pep Guardiola was full of praise for the Blades in the build up to the match and on Tuesday night it was clear to see why.
The on-loan Manchester United goalkeeper saved a 36th-minute penalty from Gabriel Jesus and saved well to deny Raheem Sterling and Nicolas Otamendi, before substitute Aguero scored in the 73rd minute to give City victory.
Guardiola sprung a surprise by naming Laporte in his starting line up, with the key defender having been out with a knee injury since the end of August.
There would have been some concern in the visiting dugout after 13 minutes when the Frenchman was caught with a scything tackle by Mo Besic – a challenge that earned the on-loan Everton midfielder a yellow card – but he played 78 minutes before being replaced.
The champions have looked suspect at the back in Laporte's absence and if the assumption was that his return would bring back stability to the defence then those assertions appeared wrong early on.
City were exposed when Oli McBurnie rolled Laporte and flicked the ball in behind the defence for Billy Sharp. It was a good chance for the Blades but their captain saw his cross intercepted by Fernandinho as he tried to pick out the unmarked John Fleck.
The visitors threatened for the first time after 20 minutes. Chris Basham lost the ball on the half-way line, allowing Riyad Mahrez to break. He picked out Sterling in the penalty area but his effort was brilliantly saved by Henderson, flinging himself to his right.
Henderson was busy again shortly afterwards to block an acrobatic volley by Otamendi as City began to get on top.
They were presented with the opportunity to make their pressure count when Mahrez went down under a combination of challenges from both Basham and John Egan. However, Henderson saved Jesus' penalty, diving to his right to beat away the ball.
Guardiola was enraged as the goalkeeper was a couple of yards in front of his line when making the save. VAR official Andy Madley saw nothing untoward, with the technology unable to rule on such decisions.
City noticeably upped their tempo at the beginning of the second half, their passing was more incisive and their movement much improved.
The Blades remained strong as a defensive unit, however, and when City did carve out their first chance of the second half after an hour, Henderson was on hand again to keep out Jesus' header.
But Wilder's side gave as good as they got. Some lovely one-touch football down the right ended with substitute Lys Mousset sending a back-heel into the arms of Ederson, after the City goalkeeper had pushed the ball into his path from a cross.
McBurnie was then inches away from turning home Enda Stevens' low cross as he slid goalwards.
City went straight down the other end and scored. A teasing cross from Kevin De Bruyne, pitched perfectly between Henderson and his defenders, was tapped home from inside the six-yard box by Aguero, who had only been on the pitch for six minutes.
Rodri came close to quickly doubling the lead but he flashed his header from a corner over the crossbar.
Some typically solid defending by Jack O'Connell denied Sterling a goal but City bounced back from the disappointment of Saturday's home draw with Crystal Palace.