The Swans were beaten 2-0 in their first home game of the season after Hull City kept up their 100 per cent record.
It proved a hugely disappointing afternoon for the Swans, who had struck the crossbar after just six minutes via Gylfi Sigurdsson.
Despite having the vast majority of possession and territory, the hosts failed to find the quality finish.
Hull, who beat champions Leicester City on the opening weekend, picked up another victory thanks to goals in the second half from sub Shaun Maloney - in the 79th minute - and Abel Hernandez in added on time.
The Swans made one change to their starting XI.
Leon Britton, who captained the Swans in last week's 1-0 win at Burnley, missed out through illness so Gylfi Sigurdsson made his first start after coming off the bench at Turf Moor.
With Britton unavailable, Jack Cork wore the captain's armband while South Korean Ki Sung-Yueng was named among the substitutes as he hoped to make his first appearance of the season.
SWANS: Lukasz Fabianski, Kyle Naughton, Federico Fernandez, Jordi Amat, Stephen Kingsley, Jack Cork (capt), Leroy Fer (Ki Sung-Yueng, 68), Gylfi Sigurdsson, Wayne Routledge (Jefferson Montero, 55), Modou Barrow (Nathan Dyer, 85), Fernando Llorente.
SUBS: Kristoffer Nordfeldt, Angel Rangel, Mike van der Hoorn, Jay Fulton.
HULL CITY: Eldin Jakupovic, Andrew Robertson, Curtis Davies (capt), David Meyler, Tom Huddlestone, Abel Hernandez, Robert Snodgrass, Sam Clucas, Jake Livermore, Adama Diomande (Shaun Maloney, 73), Ahmed Elmohamady.
SUBS: Dusan Kuciak, Josh Tymon, Jarrod Bowen, Greg Luer, Greg Olley, Josh Clackstone.
It proved an exciting opening half hour, with the Swans primarily on the attack.
Watched by new majority shareholders Jason Levien and Stephen Kaplan, who were taking in their first game at the Liberty since taking a major stake of the club, the Swans went within inches of opening the scoring after just six minutes.
That came when Wayne Routledge teed up Gylfi Sigurdsson, and the Icelandic star struck a sweet 20-yard half-volley which was tipped onto the crossbar by Eldin Jakupovic.
Jordi Amat then drove a low 30-yard effort, which flew wide, while Fernando Llorente -making his home debut - headed wide from Kyle Naughton's cross.
At the other end, Adama Diomande rifled his effort wide from inside the 18-yard box following a swift counter from the visitors.
The Swans kept plugging away, and Leroy Fer curled an effort wide after Llorente's neat slip pass, before Jack Cork's low shot bounced wide with Jakupovic untroubled.
The lively Modou Barrow, who was causing problems down Hull's left flank, then crossed to Routledge, but the winger's backheeled effort was off target from 12 yards.
Then it was Routledge's turn to cross, with his delivery meeting Llorente ten yards out, but the big Spaniard could only head his effort over the crossbar and onto the top of the net.
The Swans then survived a penalty scare after a Jordi Amat challenge on Robert Snodgrass, which saw the Scot need treatment, was waved away by referee Stuart Attwell.
That proved to be the last real action of the first half, with both teams going into the break on level terms.
HALF-TIME: Swans 0 Hull City 0
The Swans failed to replicate their fine start to the first half as they came up aganist a well-organised Hull backline.
Naughton drove a 25-yard effort low and wide, while, at the other end, Snodgrass was denied by fellow Scot Stephen Kingsley as the latter deflected his shot wide for a corner.
Fer was the next to be denied as his goalbound shot was nudged wide while Sigurdsson's corner was sliced just past the near post by Curtis Davies.
Then, with 11 minutes to go, the visitors took the lead.
In came the corner, and after taking an initial touch in a crowded box, the ball deflected off sub Shaun Maloney and into the net from two yards out.
The lead could, and should, have been doubled as Abel Hernandez raced in on goal after latching onto a loose ball, but he was denied by a fantastic reactive save from Lukasz Fabianski.
But, in added on time, Hull did make sure of the points as Maloney beat the offside trap to latch onto a pass and he tapped it to Hernandez, who fired past Fabianski from close range.
That wrapped up a hugely disappointing afternoon for the Swans, who fell to their first defeat of the season.