Darren Pratley marked his return from suspension by heading the opener midway through a first period which the hosts completely dominated, with Brendan Rodgers’ side continuing the free-flowing football which earned them plaudits under previous managers Roberto Martinez and Paulo Sousa.
And they looked destined for all three points when Scott Sinclair capitalised on an awful back pass from Sky Blues substitute Martin Cranie just two minutes after the restart.
But Ben Turner’s second goal of the season from a Coventry corner ignited a new air of confidence in the visitors.
But, despite plenty of pressure, they failed to snatch a share of the spoils and will welcome the arrival of Marlon King should protracted talks over a deal for the striker be ironed out.
The influential Pratley returned to Swansea’s midfield having missed Saturday’s 2-1 defeat at Leeds, while Joe Allen was handed a start after his impressive cameo at Elland Road.
Iceland international midfielder Aron Gunnarsson came into Coventry’s XI as the only change from the 1-1 draw against Leicester.
The Sky Blues were firmly on the backfoot for the majority of the M69 derby and it was very much the same story for Aidy Boothroyd’s outfit in the first half in south Wales.
Midfielder Allen fired just off target shortly before the hosts got the goal their early dominance deserved with 19 minutes on the clock.
Mark Gower floated over a corner from the right and Pratley found himself unmarked near the penalty spot to head past Keiren Westwood.
The lively Nathan Dyer could and maybe should have quickly made it 2-0 but he spent too long measuring his goalbound shot from 12 yards and allowed Sammy Clingan to get in and produce a saving block.
Coventry offered brief passages of promising play over the remainder of the first half but it was Swansea who remained firmly on top and were getting through the visiting defence with alarming ease – Pratley twice going close to doubling his tally.
Boothroyd looked to switch things around at the break and introduced full-back Cranie into a changed 4-4-2 system but it was his touch after just 68 seconds that handed Swansea their second.
The former Pompey man played an awful back pass which only found Pratley, he saw his shot bounce back off a post and fortunately into the path of Sinclair who duly found the net.
Dyer again hesitated somewhat when given the chance to add a third, before Swans skipper Garry Monk cleared off the line from Lukas Jutkiewicz at the other end.
And from the resulting corner, Coventry grabbed themselves a lifeline when Turner prodded home a header from defensive partner Richard Wood.
The goal certainly raised visiting spirits and Monk was forced to desperately clear his lines before Jutkiewicz and Gunnarsson both went close as the second half wore on.
Westwood produced a stunning save to deny Dyer a killer third late on but, nevertheless, the Swans held on to leave Coventry still waiting for a first win in Swansea since 1950.