Rodri's goal a minute from time secured victory for Manchester City shortly after Jayden Bogle's strike seemed set to give Sheffield United their first point of the season.
Erling Haaland missed a penalty in the first half but opened the scoring just after the hour mark to seemingly send City on their way to victory at Bramall Lane.
The Norwegian striker had endured a game to forget before the goal, as his spot kick came back off the post, he missed the target with one glaring chance and saw Wes Foderingham also deny him with a fantastic stop.
Jack Grealish laid the ball on a plate for Haaland's goal, chipping to the far post where Haaland could just nod home.
An error from Sheffield-born Kyle Walker gifted United possession in the CIty area five minutes from time and the ball eventually found its way to substitute Bogle whose deflected effort flew into the far corner.
That sprung the champions into relentless attack and Walker made amends, getting to the by-line and pulling back for Rodri who blasted the ball into the top corner.
City stand atop the table with three wins from three, while The Blades lie fourth-bottom.