Manchester City got back to winning ways in the Premier League with Kyle Walker's first-half effort enough to see off his boyhood club in tricky conditions at Bramhall Lane.
The result flattered the hosts who remain without a win through their opening seven games of the season.
Story of the match
The conditions at Bramhall Lane certainly suited the host's direct style of play, with the heavy concentration of water causing the ball to hold up as Manchester City looked to play their traditional tiki-taka football.
Regardless of the issues with the weather, it was Manchester City who dominated the run of the play in the first half, with their first real opportunity falling the way of makeshift striker Ferran Torres after just nine minutes.
Joao Cancelo's deep cross from the left flank found the Spaniard 12 yards out but his header was palmed away by Aaron Ramsdale.
Despite being brought in as a winger, Ferran was starting upfront for his second consecutive game, having been asked to play that central position in Marseille in the week due to the injuries to both Sergio Aguero and Gabriel Jesus.
He soon found himself with another opportunity to open the scoring. It came following some more fine work by Cancelo and Raheem Sterling down the left flank, with the latter finding Torres at the back post.
But again he was denied by some superb work by Ramsdale, who got down quickly to deny Torres at his near post.
It was complete domination from Manchester City throughout the first half and they got the goal that their dominance warranted just shy of the half-hour mark.
Once again it came after some great work by Raheem Sterling, who utilized his pace to power away from his marker before cutting the ball back to Cancelo. The Portuguese full-back laid the ball off to Kevin De Bruyne who in turn found Kyle Walker 25 yards out.
The Englishman took one touch before powering a low driven effort that skidded along the wet turf, beating the outstretched glove of Ramsdale and nestling into the bottom corner. There was no celebration from the boyhood Sheffield United fan.
Whilst Sheffield United's forwards were mere spectators for the majority of the first half, set pieces looked a real threat for the goal-shy hosts.
There were a couple more half chances for the visitors before the break, but nothing of note as Manchester City took a one-goal advantage into the sheds.
It was more of the same early in the second half, with the hosts having completed just 158 passes to Manchester City's 358 after 55 minutes, with City looking well on their way to a first away win in the Premier League since their opening game of the season.
The pace of the game had been slowed right down as the half wore on, with Sheffield United seeing a little more of the ball than they did in the first 45, but as has been the case for the Blades for the majority of the season so far, they were failing to create any real opportunities from open play.
Their first real opportunity of the game came in the 70th minute. Sander Berge skipped past Cancelo down the right-hand side before cutting the ball back to John Lundstram on the edge of the box.
Unfortunately for the hosts, Lundstram was leaning too far back when he made a connection with the ball, with his first-time effort flying over the bar.
Shortly after it was Rhian Brewster who found himself in on goal, being sent through one-on-one, but his tame, chipped effort was comfortably dealt with by Ederson. The flag later went up so the goal wouldn't have counted regardless.
Chances were few and far between in the latter stages, with both sides making changes as Manchester City looked to prevent Sheffield United finding any route back into the game.
Ramsdale had to be alert to stop Sterling from getting on the end of Ederson's long ball forward, with the Englishman showing great composure to stay within the confines of his own box and palm the ball away from the onrushing City forward.
Despite an improved second-half performance, Sheffield United were unable to find an equaliser - they didn't have a single shot on target all day - as they remain with just the one point through the opening seven games of the season.
Meanwhile, it's back-to-back wins and back-to-back clean sheets for Manchester City, who followed up the midweek win over Marseille with a complete display that takes them up to seventh in the Premier League standings.
Ferran the man
When Sergio Aguero failed to return to the pitch for the second half at the London Stadium, many questioned how City would cope without a striker for the second time this season.
Well, the answer is simple. Ferran Torres.
The Spaniard may not have been on the scoresheet in today's win - largely due to the fine performance of Ramsdale - but he was a nuisance for the Sheffield United backline all day.
His movement is second is none, whilst his ability to drop deeper and get involved with attacks helped to create the space out wide for Mahrez and Sterling to do their thing.
It's only early days for the Spaniard in that false nine role, but the early signs are very, very promising.
United's goal struggles continue
Losing to Manchester City isn't the end of the world - these aren't the games that keep you up - but the goal problems are becoming a real issue at Bramall Lane.
Just three goals for the Blades in their opening seven games, with Rhian Brewster still to get off the mark.
Wilder's men have Chelsea, West Ham and West Brom to come over the next three rounds of fixtures. They'll need to find their scoring boots soon or the side that finished ninth last season could find themselves in real trouble at the wrong end of the table.