Ki Sung-Yueng had given the Swans the lead against the run of play after 18 minutes, before Bafetimbi Gomis acrobatically doubled the Welshmen’s lead on 37 minutes.
Hull pulled one back through Paul McShane’s close-range strike five minutes after the break, but their task was made even tougher when David Meyler saw red card for a reckless lunge on Kyle Naughton, who limped off as a result.
Swansea looked in control from that moment on and made sure of the points in stoppage-time through Gomis, Garry Monk’s side just two points off bettering their Premier League points record after another win.
Steve Bruce’s men began the day just three points above the bottom three but looked like they were about to build on their spirited performance against Chelsea last time out after a bright start, without troubling Golden Glove-chasing Lukasz Fabianski in the hosts’ goal.
But they could not make their possession count and after allowing Jonjo Shelvey far too much time to line up the shot, Alan McGregor could only parry the midfielder’s effort into the path of the onrushing Ki, who had the simple task of side-footing into the net from a six yards.
The goal was a hammer blow to the Tigers, but they only had themselves to blame for going further behind.
A corner was floated in from the right, but after several attempts, Hull could not get the ball clear and only diverted the ball into the path of Gomis, who brilliantly dispatched an overhead kick to double the home side’s lead.
After the break, Hull again came out of the blocks and almost immediately got themselves back into the match.
Robbie Brady curled a dangerous free-kick into the box, Alex Bruce got up first to flick the ball on, and McShane beat Fabianski to the ball to prod home to get the Tigers back in the contest.
Then, just as the momentum seemed to have swung in the visitors’ favour, Meyler inexplicably lunged at Naughton, with his studs high, leaving referee Andre Marriner no choice but to brandish the red card.
Abel Hernandez had a golden opportunity to get Hull back in it against the run of play, but he could not get the right connection when in acres of space in the box.
And that miss proved costly as the excellent Gylfi Sigurdsson lofted the ball over the top to Gomis, who had the time and space to stride towards goal and loft the ball over McGregor to seal victory in the dying moments, and leave Hull with it all to do to ensure their survival.
Phil Thompson’s verdict:
“It was a poor start to the game, both teams jousting in midfield to get control. It was boring, both keepers had nothing to do. Then bang, out of the blue, Jonjo Shelvey has a shot, McGregor parries it and Ki puts it in. 37 minutes, it’s 2-0, Gomis. A corner comes in, gets headed out, and when the ball comes back in, he’s actually in an offside position. But it goes on and he puts it in with an overhead kick. In the second half, we’re all thinking, ‘what is Steve Bruce going to do here?’
“I imagine Steve will be angry at the outcome (of the red card). Meyler has led with his wrong foot, right across with his left foot, and he catches the top of the ball which accelerates his movement into the shin of Kyle Walker. I’ve seen it a few times, and people might say it’s a bit unfortunate because he’s got the ball, but it’s excessive force. I think the referee has got it right.”
Swansea: Fabianski (6), Naughton (6), Fernandez (7), Williams (7), Taylor (7), Ki (7), Cork (7), Shelvey (6), Routledge (6), Gomis (7), Sigurdsson (8).
Subs: Dyer (6), Grimes (5), Rangel (6).
Hull: McGregor (6), Dawson (6), Bruce (6), McShane (7), Elmohamady(6), Ramirez (5), Livermore (5), Meyler (3), Brady (7), N’Doye (6), Hernandez (4).
Subs: Diame (5), Sagbo, Aluko (5), Quinn (6).
Man of the match: Gylfi Sigurdsson.