Man City 2-0 Sheff Utd - Highlights
Despite missing Erling Haaland for a seventh consecutive game due to a foot injury, City were never troubled by the bottom-of-the-table Blades.
Rodri ended Sheffield United's resistence after just 14 minutes when the Spanish midfielder surged forward and fired low into the far corner.
Julian Alvarez again ably filled Haaland's shoes as the Argentine tapped in his fourth goal in three games to make the points safe from Phil Foden's cross just after the hour mark.
City move alongside Arsenal on 40 points, just two points behind Villa and Liverpool, who are in action at home to Newcastle on Monday.