The Blades, who are rooted to the bottom of the division, headed into this fixture in fine fettle after beating Manchester City's fierce rivals Manchester United 2-1 in their previous outing. However, while they did defend very well once again, Pep Guardiola's men did just enough to merit all three points.
Gabriel Jesus opened the scoring inside ten minutes courtesy of a fabulous bit of play by Ferran Torres.
The home side continued to dominate possession although they failed to create many clear-cut chances. Nevertheless, they were hardly troubled by Sheffield's forwards as they saw out the narrow win.
On that note, here are five talking points from the match.
#5 Manchester City's defence continues to be impenetrable
Despite resting regular first-team defenders Joao Cancelo and John Stones, Manchester City racked up yet another clean-sheet, thanks to the excellent Ruben Dias.
The Portuguese has settled in fabulously at Manchester City and has completely rejuvenated their struggling defence.
Sheffield United might not sport the most devastating offence in the league. But they did ask the Manchester City defence some serious questions with speculative lobbed passes. However, Ruben Dias had the answer to all of them, winning his aerial duels while also timing all his grounded tackles perfectly.
There is a real feeling around the club that scoring one goal might be enough to win them games, and the same could prove key in their title charge.
#4 Ferran Torres gives Guardiola selection dilemmas
20-year-old Spanish international Ferran Torres might not have replicated his Champions League heroics for Manchester City in the Premier League just yet. But he capitalised on a rare start in the competition on Saturday afternoon.
The only goal in the game was all his work, as he retained possession against all odds before setting up Gabriel Jesus to smash the ball in from point-blank range.
Although he did go missing at times, he swung in a few delicious crosses into the box. On another day, he could've had a couple of assists. His industrious performance will surely give Pep Guardiola a selection dilemma on who to pick the next time Manchester City take the pitch.