Swansea edged a relatively even contest at the KC Stadium on Saturday courtesy of a 15th-minute goal, Jonjo Shelvey's strike taking a heavy deflection off Ki Sung-yueng to leave Hull goalkeeper Allan McGregor helpless.
Steve Bruce's men were perhaps unfortunate to go in behind at half-time having hit the crossbar through Andrew Robertson, although Shelvey was also denied by the post.
The second half proved lively, with Hull's Nikica Jelavic and Shelvey both being denied by excellent saves, but one goal proved enough for Swansea, who hit the woodwork again through Bafetimbi Gomis.
Swansea's triumph was their first away from the Liberty Stadium since they surprised Manchester United on the opening day of the season.
Garry Monk's side climb to eighth in the table, while Hull - who have now gone 10 games without a win - remain in the relegation zone.
Monk named a much-changed side to the one that lost 2-1 to Tottenham last weekend, with in-form striker Wilfried Bony surprisingly named among the substitutes as one of seven alterations.
Hull made three changes of their own to the side defeated by Chelsea, two of those enforced with centre-back Michael Dawson injured and Tom Huddlestone suspended.
An end-to-end start to proceedings saw Jelavic fire well wide from a promising position to the left of the penalty area, before Wayne Routledge followed suit for Swansea at the other end.
The breakthrough came after quarter of an hour in fortuitous circumstances.
Shelvey played a one-two with Ki and chanced his arm with a 25-yard shot that cannoned off the South Korea international and beyond a wrong-footed McGregor.
It was a blow for Hull, who had started the game in a positive manner, and luck was against them once more when a wonderfully crafted move culminated in Robertson's fierce first-time shot grazing the crossbar.
The woodwork came to Hull's rescue on the half-hour, though, when Shelvey's low drive from distance rattled the inside of the right-hand post.
Hull sought a quick start to the second half and Swansea had Lukasz Fabianski - back in goal after a one-match ban - to thank for keeping out Jelavic's thumping header with a strong one-handed save.
McGregor proved equally important for Hull at the other end as Shelvey wasted a gilt-edged chance to make it 2-0 when his side-footed shot from eight yards was saved by the foot of the Scotland international.
The woodwork was once again responsible for the score remaining 1-0 in the 74th minute when Gomis' sliced volley rebounded off the right-hand post.
Aside from a tentative penalty claim from substitute Yannick Sagbo in injury time, a late Hull rally failed to materialise.
Bruce's goal-shy side have now drawn four blanks in their past five league matches, while Swansea can celebrate a first win over Hull since 2003 when they famously triumphed 4-2 to preserve their Football League status.
