Erling Haaland missed a first-half penalty, but opened the scoring just after the hour mark with a powerful header.
Jayden Bogle equalised for the hosts with five minutes of normal time remaining, before Rodrigo‘s stunning left-foot effort crashed into the top corner to secure all three points for Pep Guardiola‘s side.
The Spaniard, who now has two goals in our opening three league matches, was pleased with the team’s fighting spirit despite the Blades’ late leveller.
“Yeah, we worked a lot today,” he said. “It’s one of the games where you have to be patient until the end because they’re very narrow.
“Great credit to them. They defended so good today. In the end, we had the first chance with the penalty and unfortunately we missed.
“But we kept trying and trying till the end. Erling [Haaland] needed one, two, three chances but he is a goalscorer and he scored for us.
“The mistake for the goal cannot happen again. The mentality of the game didn’t drop, we kept going and at the end I got the goal so I am very happy.”
As the clock ticked past the hour mark, it seemed to be one of those days for City, with a combination of miscued finishing, superb goalkeeping and last-ditch defending keeping us at bay at Bramall Lane.
Rodrigo, who had a few sighters at goal before the opener, was happy to see the patience pay off in front of goal.
“Sometimes football is like this,” he declared. “You try for 90 minutes, score one goal and one mistake gives you a draw. But this is football.
“We know the level of this league. You cannot drop or make mistakes in these situations.
“There’s no regrets for the team, we played good football today. We know it is a game of not many chances but at the end we won.”