Sergio Agüero came off the bench to restore normal service for Manchester City, securing a win with a sharply taken goal when the defending champions appeared in danger of being held for a second game in succession.

Certainly before Agüero’s introduction there had been little to choose between the sides, which is as much a compliment to Sheffield United as a criticism of City’s performance. And then there was Gabriel Jesus’s first-half penalty, saved by Dean Henderson. The striker has been unsuccessful with all three penalties he has taken for club and country this season, and if Pep Guardiola is going to persist with using Agüero sparingly he may like to consider giving someone else a turn from the spot.

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“I am definitely going to reflect on it,” the City manager said. “It’s not just Jesus, Agüero and Sterling have missed too, and in tight games like these penalties can make a big difference. We knew this was a tough place to come but we put in a solid performance and the big plus was the performance of Aymeric Laporte. I think he is the best left-sided central defender in the world, and when a player like that is out for five months you are bound to miss him.”

City welcomed back Laporte a few days earlier than anticipated and nearly lost him again after a mere 12 minutes when Mo Besic was booked for an untidy challenge that left the defender in a heap, though after receiving attention he was able to continue. City retained Fernandinho in a back three to match up with the home side’s formation, yet United almost found a way through in the opening minutes when Oli McBurnie played Billy Sharp behind the City backline. United briefly held a numerical advantage but Sharp was unable to pick out John Fleck with his cross.

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It was United’s turn to get lucky midway through the first half when Chris Basham miscontrolled on halfway to leave Raheem Sterling sprinting clear. The winger supplied Riyad Mahrez on the right and moved up to meet the return pass with a first-time shot, only to see Henderson dive to his right to save.

While it was a good stop by the goalkeeper United had been opened up, and from a position near the penalty spot a more accomplished finisher, Agüero say, might have scored. Henderson came to his side’s rescue again just minutes later, when Nicolás Otamendi came up for a corner and managed to improvise an aerial volley that stayed low and on target but was kept out by the goalkeeper’s legs.

Facebook Twitter Pinterest Sheffield United’s Dean Henderson dives to his right to save a first-half penalty. Photograph: Andrew Yates/Reuters

Henderson’s finest moment was still to come, because 10 minutes before the interval the goalkeeper on loan from Manchester United kept out the penalty. City had perhaps been a tad fortunate to see it awarded. Mahrez appeared to be losing control of the ball on a slalom through a crowded area by the time Basham arrived to bring his progress to an abrupt halt. With Agüero on the bench Jesus stepped up to take the kick and put it at a comfortable height for Henderson to save. The goalkeeper was a yard off his line when the ball was struck and VAR could theoretically have ordered the kick to be retaken but as applause for Henderson’s heroics were still ringing round the ground as the game restarted the officials wisely opted not to start a riot.

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The home crowd were incensed enough by half-time as it was, after seeing Ollie Norwood booked for a foul on Fernandinho when the City player had already got away with a couple of similar tactical offences without punishment.

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By the time the Brazilian did receive a caution, right on the stroke of the interval, he almost appeared to be asking Lee Mason to take action by piling into McBurnie from behind with no chance of winning the ball.

The travelling support had been singing Agüero’s name for some time before he was sent on with 23 minutes remaining. The effect was close to immediate, for with 17 minutes left the visitors were in front. All it took was one measured Kevin De Bruyne pass, expertly placed between Jack O’Connell and John Egan, and a typically well-timed Agüero run to meet the ball and tap it home.

United would have been doubly aggrieved because, moments before, McBurnie had narrowly failed to connect with a similarly inviting cross from Enda Stevens after Kyle Walker had lost the ball, though replays gave the impression a goal might not have passed a VAR offside test.

“When top sides come here we want them to go through the mixer to get a result,” Chris Wilder said. “We went toe to toe with City and that’s something to be proud of but they have real quality and they won through a world-class pass and a fabulous finish.”