The City right-back struck a low shot home midway through the first-half in a game largely dominated by Pep Guardiola's side.
Though City had 16 shots on goal, the three points and another clean sheet mean it will be a happy trip back across the Pennines for Guardiola's men.
City looked bright and up for the challenge straight from the kick-off and could have been ahead on eight minutes as Joao Cancelo’s cross was glanced goalwards by Ferran Torres but Aaron Ramsdale palmed the effort away.
Raheem Sterling was a constant problem down the left for the Sheffield United defence and his clever threaded pass to Torres again produced a good save from Ramsdale as the Spaniard toe-poked an effort from close range.
As the half wore on, City’s dominance grew and on 28 minutes, the deadlock was broken with a richly deserved goal.
Sterling was the architect, wriggling away from a couple of challenges on the halfway line before heading towards goal, before finding Kevin De Bruyne who quickly played it in to the feet of Kyle Walker who fizzed a low shot into the bottom left corner.
Walker, superb all season, barely celebrated with his rare strike coming against the club he supported as a lad, and on his 100th Premier League appearance for City.
It was to be the only goal of the first half at a wet and windy Bramall Lane.
The pattern of play continued after the break but though City kept creating chances, the second goal needed for security wouldn’t come.
Riyad Mahrez was unlucky not to see his free-kick go in, with Ramsdale making another fine save and De Bruyne struck a low shot inches past the post - both before the hour mark - but so long as there was only one goal in it, the hosts were still in the hunt.
There was a slower pace to the game as time wore on, with City well on top but the hosts occasionally threatening.
Ederson very nearly had an assist to his name with an incredible 70-yard pass almost putting Sterling in on goal but the impressive Ramsdale intervened just in time with a header almost on the ground at the edge of the box.
But it was Walker’s goal – fittingly – that settled the game that was hardly a classic, but a valuable win over Blades side who will surely find their mojo before too long.
WAlker's excellent start continues
Kyle Walker has started the new season in the from of his life.
The England right-back must be one of the first names on Pep Guardiola's team-sheet with his pace and power a vital component of City's defence.
It's hard to think of a better right-back in world football at present, such has been the level of Walker's displays this campaign.
He may not be known for his goal-scoring, but when he does find the net, they're usually a bit special and to score at Bramall Lane will have been extra special for the boyhood Blade - even if it will leave him with mixed feelings.
Sheffield United: Ramsdale, Basham, Egan, Stevens, Baldock, Berge, Ampadu (Norwood 65), Osborn (Lundstram 55), Lowe (McGoldrick 81), Brewster, McBurnie
Subs: Sharp, Burke, Robinson, Verrips
City resume Champions League group stage action on Tuesday evening with a home clash against Olympiakos (8pm).
Then it’s another home game against Liverpool the following Sunday (4.30pm kick-off).
What it means...
We'll have to wait until all the weekend's games are complete to see how City sit in the table, but after this game we sat seventh in the Premier League on 11 points - two off the top - and with a game in hand over many clubs.