Alvaro Negredo’s header and Yaya Toure’s late free kick gave the 2011-12 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.
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 to a scoreless draw by Cardiff.
SERIE A: Juventus cruised to a 4-1 victory over 10-man Lazio as the capital club fell to another hefty defeat at the hands of the defending champion.
Two world-class finishes from Arturo Vidal sent Juventus on its way to another victory.
Lazio was forced to play nearly half an hour with 10 men after Hernanes was sent off for a second yellow card.
Last year’s runner-up, Napoli, beat Chievo Verona 4-2.
BUNDESLIGA: Schalke ended Bayer Leverkusen’s winning start with a 2-0 victory that relieves the pressure on coach Jens Keller following the club’s poor league start.
Earlier, Hamburger SV defeated promoted Eintracht Braunschweig 4-0 to buy Thorsten Fink some breathing space after his side mimicked Schalke’s start to the season.
In other games, Hannover came from behind to defeat Mainz 4-1 and end the visitors’ winning start to the season. Borussia Moenchengladbach beat Werder Bremen 4-1, with Juan Arango opening the scoring in the 36th and Raffael scoring off a rebound in the 53rd. Wolfsburg defeated Hertha Berlin 2-0 through Ivica Olic’s 42nd-minute strike, and a penalty earned and converted by Diego before the break. Kevin Vogt’s 84th-minute goal was enough for Augsburg to win 1-0 at Nuremberg.
LA LIGA: Celta Vigo’s lack of finishing touch condemned it to a 1-1 draw at home against Granada, while Valladolid beat Getafe 1-0 for its first points of the season.
LIGUE 1: Zlatan Ibrahimovic ended his scoring drought as Paris Saint-Germain scored twice in injury time to secure a scrappy 2-0 home win against newly-promoted Guingamp.
Earlier, Lyon’s losing streak increased to four matches after being defeated 2-1 at Evian.
In Saturday’s other matches, it was: Bastia 2, Toulouse 1; Lorient 1, Valenciennes 0; Reims 0, Nantes 0; Rennes 0, Lille 0, and Sochaux 0, Ajaccio 0.