Swansea's theoretical Championship play-off hopes were ended as Hull came from two goals down to earn a 2-2 draw at the Liberty Stadium.
Scotland striker Oli McBurnie scored in either half to move to 23 goals for the season and put the home side two up.
Hull, with an unfamiliar line-up as they prepare for next season, were subdued in attack but managed to grab a point thanks to second-half strikes from top scorer Jarrod Bowen and substitute Nouha Dicko.
It meant Swansea were unable to make it a seventh straight win on home soil.
Wayne Routledge had a shot blocked after just 27 seconds as Swansea went straight on the attack.
The hosts had all the possession but Nigel Adkins' Tigers were given an opportunity when Swansea played out from the back and lost possession, only for Jackson Irvine to volley wide.
At the other end a mix-up in the Hull defence gave Routledge a second opportunity. He cut inside, but his shock was blocked brilliantly by Jordy de Wijs and went out for a corner.
From the set-piece, Connor Roberts' curling effort was kept out by an acrobatic George Long save.
McBurnie failed to connect with a Roberts cross, but he put Swansea ahead in the 37th minute.
Hull's Kamil Grosicki went down in the box under a Mike Van Der Hoorn challenge but referee Geoff Eltringham waved away penalty appeals and Swansea responded.
Roberts, Nathan Dyer and Routledge were all involved in a quick passing move which ended with McBurnie tapping home from close range.
McBurnie had a header saved before the break as he pushed for a second of the day and Hull swapped former Swansea man Stephen Kingsley for youngster Brandon Fleming at the break.
They should have levelled when Bowen led a Hull breakaway and fed Grosicki in space, but his finish was awful as he ballooned the ball over the bar.
Hull captain Markus Henriksen was booked for wiping out McBurnie, but the striker had the last laugh when he made it 2-0 in the 66th minute by nodding home a pinpoint Dan James cross.
Hull cut the deficit 11 minutes later as Bowen poked home his 22nd goal of the season from De Wijs' flick-on as Swansea appealed in vain for an offside flag.
Routledge shot straight at Long from a James pass and the miss proved crucial as Dicko converted a cross from his fellow replacement Jon Toral to level the scores.
Swansea thought they had won it late on when Jay Fulton headed Matt Grimes' corner on target, but Irvine cleared off the line and Eltringham had already blown the whistle.