The Swans secured their second away win of the season thanks to Ki Sung-Yueng's goal at the KC Stadium.
In a game of few chances, Jonjo Shelvey's shot cannoned off the South Korean and rolled into the net past Allan McGregor.
The home side failed to really test Lukasz Fabianski, and the visitors could have won by a greater margin.
Shelvey struck a post in the first half, while Bafetimbi Gomis saw a second-half effort also come back off the woodwork.
Garry Monk made seven changes to the side that lost to Spurs last time out.
Lukasz Fabianksi returned in goal, while Federico Fernandez and Jazz Richards came into the back four.
Leon Britton (knee), Gylfi Sigurdsson (foot) and Jefferson Montero (hamstring) all missed out with slight knocks meaning Tom Carroll, Jonjo Shelvey and Nathan Dyer all started for the visitors.
Wilfried Bony dropped to the substitutes bench as Bafetimbi Gomis led the line.
Hull, meanwhile, made three changes to the side that lost to Chelsea as Alex Bruce, Gaston Ramirez and Abel Hernandez come in for Michael Dawson, Tom Huddlestone and Sone Aluko.
HULL: Allan McGregor, Alex Bruce (Sone Aluko, 60), James Chester, Curtis Davies (Harry Maguire, 76), David Meyler, Abel Hernandez, Jake Livermore, Nikica Jelavic (Yannick Sagbo, 81), Gaston Ramirez, Andy Robertson, Ahmed Elmohamady.
SUBS NOT USED: Eldin Jakupovic, Liam Rosenior, Robbie Brady, Stephen Quinn.
SWANS: Lukasz Fabianski, Jazz Richards (Angel Rangel, 81), Federico Fernandez, Ashley Williams (capt), Neil Taylor, Ki Sung-Yueng, Tom Carroll (Marvin Emnes, 57), Jonjo Shelvey, Nathan Dyer, Wayne Routledge, Bafetimbi Gomis (Wilfried Bony, 76).
SUBS NOT USED: Gerhard Tremmel, Kyle Bartley, Jay Fulton, Modou Barrow.
Both teams came into this fixture with contrasting fortunes so far this season - Hull had won just once at home while Swansea had won just once away from the Liberty Stadium.
That statistic led to a somewhat nervous start on Humberside, with Nikica Jelavic and Wayne Routledge both shooting well wide of goal having picked up good positions in the box.
Hull - second bottom of the Premier League prior to kick-off - then found themselves in trouble on 14 minutes as the Swans broke the deadlock.
Jonjo Shelvey picked up the ball 25 yards from goal and as he took aim his left foot shoot struck Ki Sung-Yueng and diverted past the helpless Allan McGregor.
That setback sparked the home side into life as Andy Robinson's shot came off the top of the crossbar, while the returning Abel Hernandez curled a left-foot shot straight into the arms of Lukasz Fabianski.
The Swans hadn't quite found their usual passing rhythm in the opening stages but came close to extending their lead just past the half hour mark as Shelvey found space outside the box before seeing his low shot come back off the post.
Half-time: Hull 0 Swans 1
Neither side made any changes at the break, but it was Hull who had the first chance of the second period as Gaston Ramirez's free-kick from just outside the penalty area was a fraction too high as it landed on the roof of the net.
The hosts came close again on 54 minutes as Ahmed Elmohamady's cross from the right was met by Nikica Jelavic, but his effort was parried clear by Fabianski.
At the other end, Allan McGregor prevent Swansea from doubling their lead as a flowing move saw Ki roll the ball across the box for the unmarked Shelvey, but his strike was straight at the goalkeeper.
The visitors made their first change of the afternoon as Tom Carroll was replaced by Marvin Emnes, and the former Middlesbrough man nearly found the net immediately as Ki's cross from the right was volleyed wide by the Dutchman.
Emnes was also involved in the Swans' next opening as he crossed for Bafetimbi Gomis at the far post but his effort bobbled towards goal and came off the post.
That was to be the Frenchman's final involvement of the afternoon as he was replaced by Wilfried Bony with 14 minutes to play.
And the Ivorian had a half chance to grab a second as he connected with Angel Rangel's cross, but his header was comfortably gathered by McGregor.
The home side failed to test Lukasz Fabianski in the closing stages and the visitors held on to claim a second away win of the campaign and move up to eighth in the Premier League table.