A James Chester own goal was enough to sink Hull and give Crystal Palace their third successive Championship win.
Chester, under pressure from Jermaine Easter, diverted Jonathan Parr's cross past Tigers goalkeeper Adriano Basso in the first half.
Easter and Parr had efforts stopped by Basso, while Hull's Matty Fryatt's drive was saved by Julian Speroni.
As Hull pressed, Aaron Mclean's header and Corry Evans' 25-yard shot were denied by Speroni and Palace held on.
Hull, looking to bounce back from the midweek defeat at Leeds, made all the early running but went behind from Palace's first meaningful attack.
Norwegian midfielder Parr whipped in a cross from the right and Chester, with Easter for company, put the ball into his own net from six yards out.
After Palace striker Sean Scannell and Hull's on-loan Manchester United teenager Robbie Brady traded long-range efforts, Basso was called into action to deny Easter and Parr, who both tried their luck from outside the area.
Hull stepped up the pressure as the first half drew to a close, with Speroni holding efforts from Tom Cairney and Robert Koren and then diving full length to deny Fryatt.
The chances dried up after the restart, but Hull winger Brady fired a fine 25-yard shot just over the bar and Cairney pulled an easy volley wide.
The Tigers picked up the tempo in the final quarter, but with Speroni on hand to stop Mclean and Evans, Palace registered their first away win since October and condemned Hull to their third league defeat of the season.