COVENTRY City slipped to their first league defeat of the season and were left to rue a first half penalty miss.
Ashley Williams' 69th minute goal sent Swansea away with all three points but it would have been a different tale had Sammy Clingan hit the target with a penalty early in the game.
Swansea started reasonably brightly and there were two good early chances for striker Stephen Dobbie.
On the first occasion his control let down as he got the wrong side of the Sky Blues' defence and then Martin Cranie made a fine challenge to keep his effort out.
Coventry created their first chance of the match when a good move ended with Isaac Osbourne crossing to the near post but Leon Best fired wide.
The Sky Blues were given a golden opportunity to take the lead when they were awarded a 13th minute penalty as Andrea Orlandi handled in the box after Aron Gunnarsson's long throw.
Clingan stepped up but cracked the spot-kick just wide of Dorus De Vries' post.
The home team carved out another chance in the 17th minute but Best's header was comfortably saved by De Vries.
Mark Gower created an opportunity for Orlandi with a clever 28th minute free-kick but his low shot was straight at Keiren Westwood, who made a solid save.
Clinton Morrison went close to adding to his season's tally of three but he headed just over after Ben Turner had helped on Clingan's free-kick.
Stephen Wright produced some superb defending just before the break to deny Gower a chance and help launch City into the Swansea half. It led to a low shot from Michael McIndoe but De Vries saved.
The Sky Blues began the second half in the ascendancy but they failed to make the most of several good openings.
Best had a 58th minute chance to repeat his exploits at Barnsley where he hammered home a free-kick, but his 25 yard effort struck the wall.
Then, on the hour mark, Gower found some space in the Sky Blues box but shot just inches wide of Westwood's upright.
After a long spell of Coventry pressure, the visitors took 69th minute lead. Leon Britton saw his acrobatic volley come back off the bar but Ashley Williams hit home for Swansea.
Jack Cork had been sent on for his Coventry debut and he hit a low effort in the 71st minute but it was comfortably held by De Vries.
There was a huge cheer as Leon McKenzie came off the bench in the 85th minute and he did well to force an 88th minute corner but the visitors managed to clear their lines and hung on for the win.
Teams
Coventry City: Westwood; Wright, Cranie, Turner, van Aanholt; Osbourne (Cork 64), Clingan, Gunnarsson, McIndoe (McKenzie 85); Best (Eastwood 84), Morrison. Subs: Konstantopoulos, Eastwood, McKenzie, Cain, Grandison, Clarke.
Swansea City: De Vries; Rangel, Monk, Williams, Tate; Dyer, Britton, Orlandi (Lopez 70), Gower, Bond (Morgan 64); Dobbie (Pintado 77). Subs: Cornell, Painter, MacDonald, Collins.
Attendance: 16,307
