Bafetimbi Gomis scored twice, the forward's second goal coming in stoppage time as Hull - hampered by a straight red card for David Meyler in the 53rd minute - threw players forward in search of a late equaliser.
The visitors came into the game knowing a win would move them six points clear of the relegation zone, but made a poor start as a goalkeeping error from Allan McGregor enabled Swansea to take the lead after 18 minutes.
McGregor failed to deal with a long-range Jonjo Shelvey effort, presenting Ki Sung-yueng with a chance that he did not waste, and a magnificent acrobatic finish from Gomis in the 37th minute seemingly put Swansea in complete control.
Paul McShane pulled one back five minutes after the interval, but Hull's momentum was soon checked as Meyler was sent off for a rash challenge on Kyle Naughton.
Gomis added a third for Swansea late on to complete a miserable day for Steve Bruce's side.
After a slow start to proceedings, Ki broke the deadlock as he turned home a rebound from Shelvey's 25-yard strike, which McGregor could only parry into the South Korea international's path.
Hull were dealt a further blow on the half-hour mark when Gaston Ramirez - who had been a doubt prior to the game due to a hamstring issue - limped off to be replaced by Stephen Quinn.
Swansea continued to have the better of the play despite flashes of attacking initiative from the visitors, and saw their lead doubled courtesy of a superb second from Gomis.
The former Lyon man brilliantly found the net with a stunning scissor-kick after Hull had allowed the ball to be played back into the box following a corner.
Tempers flared shortly after the restart, with Ashley Williams booked for a foul on Dame N'Doye, who was then cautioned himself following a coming together with Wayne Routledge.
The visitors took advantage of the resulting free-kick, McShane tapping home after Alex Bruce had flicked on a terrific delivery from Robbie Brady - who had taken Andrew Robertson's place in the starting XI.
Another Brady delivery caused chaos in the Swansea box as the hosts were forced to scramble clear from a Bruce header, but the pendulum swung again when Meyler saw red.
The ex-Sunderland midfielder dived in to a challenge with Naughton as he tried to win a loose ball but only succeeded in driving his boot into the right-back's leg.
Referee Andre Marriner showed no hesitation in dismissing Meyler and the injured Naughton was replaced by Angel Rangel.
Hull never really threatened to overcome their numerical disadvantage and conceded a third as Gomis latched on to a long ball over the top and lifted a delicate lob over McGregor.
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