Following four defeats in their previous five Premier League outings, Steve Bruce's men needed a morale boost ahead of next weekend's FA Cup semi-final against League One Sheffield United at the English national stadium, and they got it by moving further clear of the relegation zone.
George Boyd, returning from a three-match suspension, towered above Angel Rangel to head home the only goal – his first since December – six minutes before half-time.
Bruce had urged the home supporters to recreate the atmosphere that propelled Hull to promotion from the Championship last season, and they were fully behind their team despite Swansea having the better of possession and the chances early on.
Just 10 years ago to the month, Hull won 3-2 at Swansea in the fourth tier of English football, and the Welsh side still have some work to do to retain their Premier League status, with an 11th successive away league match without victory keeping them only just above safety.
Swansea named an unchanged side, while Hull welcomed Maynor Figueroa and Boyd back into their starting XI following injury and suspension respectively.
Figueroa was quickly involved, producing a superb cross to give Shane Long a glorious chance, but the Republic of Ireland striker’s tame shot allowed Michel Vorm to push the ball behind for a corner.
Long responded positively on 16 minutes, however, controlling the ball with an exquisite touch and teeing up Boyd, whose low shot from the edge of the box forced Vorm into a comfortable save.
Figueroa, renowned for scoring from his own half for Wigan Athletic against Stoke City in 2009, tried his luck from 45 yards with another audacious attempt, but the ball went out for a throw.
The pace of Wayne Routledge and Jonathan de Guzman tormented Hull from the outset, and the former’s delightful throughball sent the latter racing into the area after 25 minutes. De Guzman cut inside his marker, but he hesitated and his shot was blocked.
Almost immediately, Wilfried Bony threaded the ball behind the hosts’ defence for Routledge. Noticing Steve Harper well off his line, Routledge attempted a chip but his weak effort went straight into the arms of the 39-year-old goalkeeper.
Nikica Jelavic then fired a free-kick narrowly over before Hull broke the deadlock six minutes before half-time.
Liam Rosenior crossed to the back post and as Vorm stayed on his line, Boyd towered above the static Rangel to head home and leave the Swansea goalkeeper and right-back arguing.
Soon after the restart, Boyd tricked his way down the flank and delivered a threatening cross, which Long just failed to get his head to.
Thereafter, Swansea began to dominate possession, but despite some neat passing they failed to create a meaningful chance until the 70th minute, when substitute Nathan Dyer sliced his strike well wide after impressive play from Routledge.
Swansea's last chance fell to Bony, but after racing onto a pass from Jonjo Shelvey the Ivorian's wayward shot from inside the area went high and wide as Hull held on for a much-needed win.
