Sammy Clingan missed a first-half penalty for Coventry
An Ashley Williams strike gave Swansea their first league win under manager Paulo Sousa and ended Coventry City's unbeaten start to the season.
The hosts blew a penalty, Sammy Clingan firing wide after Andrea Orlandi handled Aron Gunnarsson's long throw.
Swansea had got the better of the game with some confident play, though.
Their reward came after the break when a superb Nathan Dyer strike clattered the bar, falling to Williams who drove home across keeper Keiren Westwood.
The victory was Swansea's first at the Ricoh Arena and only their second at Coventry, the first coming back in 1949.
Coventry manager Chris Coleman: "We didn't lose the game because of the penalty. If we had been on the front foot in this game, we would have got a result.
"That is no disrespect to Swansea because they play good football and have a good manager but we can be better than that.
"That's our fifth game in 13 days so there is maybe a bit of fatigue creeping in but I am not going to make excuses.
"We had one or two under-performing so we hope to have another face in early next week to put a bit of pressure on."
Sousa delight at Swansea victory
Swansea manager Paulo Sousa:
"This was not a relief and I believe we can grow much more than we have up to now.
"If we have the desire like that we will get more points. What I want and expect from my team is to be competitive and in the top 10 at the end of the season.
"It is not a concern that the strikers are not scoring. If you look at the last game every player is having opportunities and in my opinion that is the important thing. I just hope we start scoring them."
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