Hull suffered a first home defeat under Marco Silva at the most inopportune moment as their survival bid was hampered by relegated Sunderland.
The hosts created several chances, only for Lazar Markovic and Abel Hernandez - most notably - to be denied by impressive away keeper Jordan Pickford.
Sunderland took advantage to go ahead through Billy Jones' close-range diving header after John O'Shea's flick-on from a corner.
And the Black Cats sealed their first win in 11 league matches when Jermain Defoe converted from close range.
The Tigers remain two points ahead of third-bottom Swansea, who play later on Saturday against Everton.