Raheem Sterling scored his first goal for the club and Fernandinho netted a superb second to lift City to their fourth successive win and open an eight-point advantage over Chelsea.
Liverpool, who had taken seven points from their opening three games, slumped to a surprise 3-0 home defeat by West Ham United and had midfielder Philippe Coutinho sent off.
Newcastle United's Fabricio Coloccini scored an own-goal as Arsenal laboured to their second win of the season with a highly-charged 1-0 victory over their 10-man hosts at St James' Park.
Sunderland remained bottom after an eventful 2-2 draw at Aston Villa and promoted Bournemouth drew 1-1 with Leicester City after Jamie Vardy cancelled out Callum Wilson's fourth goal in two games.
Club-record signing Salomon Rondon scored to give West Bromwich Albion a 1-0 victory over Stoke City who had Ibrahim Afellay and Charlie Adam sent off.