Alvaro Negredo's header and Yaya Toure's late free kick gave the 2012 champions an unconvincing 2-0 victory over Hull.
After starting the season with an electrifying 4-0 rout of Newcastle, City lost at Cardiff last weekend to drop points early in its bid to reclaim the title from Manchester United.
United is in action at Liverpool on Sunday when Arsenal hosts Tottenham in the north London derby.
In their third matches of the season on Saturday, a trio of teams produced their first victories.
There were 1-0 wins for Newcastle over Fulham and Norwich against Southampton, while newcomer Crystal Palace earned its first points of the season by beating Sunderland 3-1.
Stoke made it two wins in three games by defeating West Ham 1-0, while Everton was held 0-0 by Cardiff, the Merseyside team's third successive league draw under new manager Roberto Martinez.
At the Etihad Stadium, City laboured against a resilient Hull side until Negredo, an off-season signing from Sevilla, came off the bench to head in Pablo Zabaleta's cross in the 64th minute.
Yaya Toure put the victory beyond doubt in the 90th minute when he curled in a free kick after Samir Nasri was fouled.
"We must improve," City manager Manuel Pellegrini said. "We had too many difficulties in the first half (in creating chances) to shoot at the Hull goal.
"They defended very well and without the movement, we need to try to be a dangerous team. Everyone told me last week (after) we lost a game to two set-pieces that I now know the Premier League, but I know the Premier League is very difficult every match."
And Palace was pleased to finally get off the mark.
Although Danny Gabbidon put the south London club ahead with a scruffy goal after nine minutes, Steven Fletcher headed Sunderland level in the 64th.
The game swung back in Palace's favour when John O'Shea was sent off for bringing down striker Dwight Gayle, who scored from the resulting penalty in the 79th.
Stuart O'Keefe completed the day's highest-scoring game with a curling shot that went into the net off the underside of the crossbar in stoppage time.
It was a more mundane win for Norwich.
Nathan Redmond scored the only goal at Carrow Road in the 68th minute by cutting in from the left to unleash a fierce drive from the edge of the box.
Jermaine Pennant scored his first goal in 63 matches as Stoke won its second match of the season.
Pennant, who had come on as a substitute at West Ham, curled a free kick over the top of the wall and beyond the reach of keeper Jussi Jaaskelainen in the 82nd.
Newcastle also left it late to produce a winner.
Hatem Ben Arfa scored the northeast club's first league goal since last season in the 86th, cutting in from the right and weaving through the defence before shooting past goalkeeper David Stockdale.Suggest a correction