Jonathan de Guzman then missed a chance to equalise for the visitors when he blazed over the bar.
Man City took advantage of that miss in the second half as Samir Nasri scored a brace to secure another home win.
Below, Sports Mole picks apart the contest at the Etihad Stadium.
On target 7
On target 4
Was the result fair?
Despite a good showing from Swansea in the first half, yes. Man City displayed their attacking intentions in the opening 30 seconds and created the better chances throughout the match. However, at times the Swans dominated possession, but they just could not make the breakthrough.
Man City's performance
Again, the attacking talents of this Man City team were crucial. Alvaro Negredo, Sergio Aguero and Samir Nasri were the main sources of danger for the Swans, especially in the second half. Although they were not at their fluent best, manager Manuel Pellegrini will be pleased with how his players got the job done. His only small concern might be the amount of time Swansea had on the ball in the first half.
If De Guzman's shot had gone in, it could have been a different game. However, he missed and Swansea failed to build on what was a very effective performance before the interval. They controlled possession and Jonjo Shelvey had a couple of long-range efforts saved by Costel Pantilimon. However, after the break they could not handle their opponents.
Sports Mole's man of the match
Samir Nasri: The former Arsenal player is starting to produce the form that made him one of the most feared attacking players in the Premier League. He scored two and was creative with the ball.
This has to be De Guzman's miss. He did the hard work, beating Martin Demichelis, but then hammered his shot over the bar with just the goalkeeper to beat.
Mark Clattenburg had a quiet 90 minutes, producing just one yellow card for Aguero's handball, which was a correct decision. He might have given a penalty when Pablo Hernandez went down in the box, but he probably got it right.
Man City: Pellegrini's men travel to West Bromwich Albion on Wednesday night.
Swansea: Swansea have a home match against Newcastle United , also on Wednesday.