Ki-Sung yueng and Bafetimbi Gomis gave Swansea a two-goal cushion at half-time which ultimately helped them move on to 46 points, just one short of their best total under Brendan Rodgers in the 2011-12 season.
Paul McShane halved the deficit five minutes after the break from a set-piece but Hull's cause was damaged almost immediately when David Meyler was sent for a reckless challenge on Kyle Naughton.
Swansea were well on top from that point but had to wait until injury time to kill the game off, Gomis running unopposed from his own half to latch onto Gylfi Sigurdsson's long ball out of defence and finish with a deft chip over Hull goalkeeper Alan McGregor.
Hull remain three points above the relegation zone but they will be casting nervous glances at the Burnley and Sunderland games on Sunday and appear to have a tricky seven-game sequence to end their season.
Liverpool, Manchester United and Arsenal all have to visit the KC Stadium while Hull's remaining away games include trips to Southampton and Tottenham.
Hull started with the urgency required from a team in their perilous position but it had faded alarmingly before Swansea scored with their first real attack after 17 minutes.
Jonjo Shelvey was afforded space 25 yards out to take aim and McGregor pushed his shot straight to Ki, who finished smartly for his seventh goal of the season and his third in his last four appearances at the Liberty Stadium.
Bruce had opted to play two strikers up top but Dame N'Doye and Abel Hernandez were being starved of service and the Tigers' ambitions were not encouraged by the sight of Gaston Ramirez limping off after half an hour.
Hull were being pushed further back and when they failed to defend a second ball from a 37th minute corner properly they conceded again.
Naughton headed the ball back into the Hull area and Robbie Brady and Alex Bruce got in a tangle for Gomis to deliver a stunning bicycle kick from 10 yards, the first time the Frenchman has scored in successive games this season following his winner before the international break at Aston Villa.
Hull had to show some passion and bookings for Hernandez and N'Doye, the latter after a tangle with Ashley Williams, suggested manager Steve Bruce had fired them up at half-time.
And they were back in the game five minutes after the break when Alex Bruce flicked on Brady's floated free-kick and McShane finished smartly from close-range.
They were almost level moments later following some pinball in the Swansea penalty area but they were reduced to 10 men after 53 minutes when Meyler flew into a tackle on Naughton and received a straight red card - Hull's sixth of the season in the Premier League.
Naughton took no further part in the game and Swansea inevitably carried the greater attacking threat after Meyler's departure, although McGregor was untroubled from distance by Shelvey and Sigurdsson.
Hull fought tenaciously to find an equaliser and always carried a threat at set-pieces but Swansea wrapped it up in stoppage time when McGregor stayed on his line instead of coming for the through ball and Gomis finished the Tigers off.
Source : PA
Source: PA