The Swans tasted their first defeat in three games as George Boyd's first-half header earned Hull City a vital three points at the KC Stadium.
The visitors failed to take the momentum from the recent draw at Arsenal and victory over Norwich in a game against a Hull side that had sat below them only on goal difference at the start of the day.
But Boyd's header, which came in the 39th minute from a Leroy Rosenior cross, proved the big difference.
It left the Swans on 33 points from as many games - six points clear of third-bottom Fulham, who had won 2-1 at Aston Villa to climb off the bottom.
The Swans remain unchanged as head coach Garry Monk stuck with the same XI that saw off Norwich City 3-0 last time out at the Liberty.
That means Michu made his third consecutive start while Jonathan de Guzman continued on the right wing and 20-goal Wilfried Bony led the line.
On the bench, there was just one change as Leroy Lita came in for Alvaro Vazquez.
Hull welcomed back George Boyd from suspension while keeper Steve Harper continued to deputise for the injured Allan McGregor.
The Tigers were also without midfielder Tom Huddlestone
HULL CITY:Steve Harper, Leroy Rosenior, Maynor Figueroa (Robert Koren, 75), James Chester, Curtis Davies (capt), David Meyler, Jake Livermore, George Boyd, Nikica Jelavic (Yannick Sagbo, 90), Shane Long (Sone Aluko, 64), Ahmed Elmohamady.
SUBS: Eldin Jakupovic, Alex Bruce, Matty Fryatt, Stephen Quinn.
SWANS: Michel Vorm, Angel Rangel, Chico Flores, Ashley Williams (capt), Ben Davies, Leon Britton (Leroy Lita, 83), Jonjo Shelvey, Michu (Pablo Hernandez, 66), Jonathan de Guzman (Nathan Dyer, ht), Wayne Routledge, Wilfried Bony.
SUBS: Gerhard Tremmel, Jordi Amat, Neil Taylor, Jose Canas.
Both sides made encouraging starts to the game, with Jonathan de Guzman volleying wide after a Jonjo Shelvey cross was cleared out to him.
Then Michu blasted over after Wayne Routledge tapped down a de Guzman cross before, at the other end, it took a superb reflex save from Michel Vorm to swat Shane Long's volley wide for a corner after Maynor Figueroa found the striker six yards out.
George Boyd then drove low at Vorm before the Swans had two decent chances to take the lead.
Firstly, Routledge's sublime through ball sent de Guzman chasing down the right, but when he cut inside his shot was blocked by a defender.
Then Wilfried Bony's deflected pass sent Routledge racing on, but his attempted chip over Steve Harper dropped straight into the keeper's hands.
Nikica Jelavic then curled a free-kick over from 20 yards while Chico Flores fired high and wide from 35 yards, before Bony drove his shot wide after David Meyler lost possession.
But the hosts took the lead in the 39th minute as a high Leroy Rosenior cross found Boyd at the back post, and he leapt above Angel Rangel to head home past Vorm from six yards.
HALF-TIME: Hull City 1 Swans 0
The Swans made a change at the break as Nathan Dyer replaced de Guzman in a straight swap on the right.
Neither side managed to create many chances, with Hull happy to protect their lead.
The Swans made another switch with 24 minutes to go as Pablo Hernandez came on in place of Michu, and the Spaniard was straight into the action as his pass found Bony, and when he teed up Jonjo Shelvey, the midfielder's shot was spilled by Harper.
Shelvey then went for goal again as he was teed up by Dyer, but he couldn't keep his effort from rising over the crossbar and into the Swans supporters behind the goal.
The Swans then carved open a fantastic opportunity to level as Routledge won possession of Figueroa and picked out Dyer, who had time to pick his spot but he scuffed wide from 18 yards.
Hernandez then drove past the near post after he earned himself some space to shoot following some fine trickery inside the Hull box.
Bony then fired wide after a neat pass from Shelvey set him up on his right foot, and then Garry Monk made his final change as Leroy Lita replaced Leon Britton, which gave the Swans a more attacking look for the remaining seven minutes.
The Swans were pushing hard for an equaliser, and they went close again as Bony and Dyer got in amongst a scramble in the box, but the ball fell kindly for Harper.
But it didn't proved enough as Hull held on for victory.