The Tigers are now only three points away from the drop after QPR's win at West Brom, having pulled a goal back on the Swans before David Meyler was shown a straight red
The hosts took the lead in the first half at the Liberty Stadium through Ki Sung-Yueng, with Bafetimbi Gomis's excellent volley doubling the score.
Paul McShane capitalised on some poor marking to turn in a free kick soon after half-time but the Tigers went down to 10 men almost immediately when David Meyler's dangerous tackle on Kyle Naughton got what it deserved.
Gomis scored his second of the day in stoppage time to confirm the result which, combined with QPR's victory at West Brom, leaves Hull just three points above the drop, while the Swans remain comfortable in eighth.
After a slow start to proceedings, Ki broke the deadlock as he turned home a rebound from Jonjo Shelvey's 25-yard strike, which Allan McGregor could only parry into the South Korea international's path.
Hull were dealt a further blow on the half-hour 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.