For the first time this season, City were without the team's Norwegian attacking star and goal machine, Erling Braut Haaland, who remained in Manchester with a minor injury.
Away at Leeds, Antoine Semenyo scored the only goal of the match in first-half added time.
With the three points, Premier League second-placed City put pressure on league leaders Arsenal. After 28 of 38 rounds, the teams are two points apart. Arsenal play their 29th league match of the season on Sunday in the London derby at home to sixth-placed Chelsea.
