Marco Silva’s side went behind after a shocking error just two minutes and 11 seconds into a game they needed to win to give themselves a fighting chance of survival.
Italy defender Andrea Ranocchia missed a simple clearance, allowing Wilfried Zaha to run clear and slot beyond goalkeeper Eldin Jakupovic.
Christian Benteke’s header doubled Palace’s lead while late goals from Luka Milivojevic, from the penalty spot, and substitute Patrick van Aanholt, completed Hull’s misery.
The Tigers, who failed to register a shot on target on Sunday, will join Sunderland and Middlesbrough in the Championship next season.
This result also means Swansea City, who were bottom of the table and four points from safety at the start of 2017, stay up.
Where did it go wrong for Hull?
Hull are back in the second tier one year after winning promotion at Wembley by beating Sheffield Wednesday in the Championship play-off final.
Their plans following a Premier League return seemed to be in disarray when manger Steve Bruce left in July following a breakdown in his relationship with vice-chairman Ehab Allam.
Mike Phelan was appointed caretaker for the start of the campaign and the former Manchester United assistant steered the Tigers to back-to-back wins. He was named manager of the month for August.
However, the season quickly unravelled with Hull winning just one of the next 18 league games before Phelan was sacked on 3 January.
The Tigers were also rocked by the loss of £10m midfield summer signing Ryan Mason to a fractured skull after clashing heads with Chelsea’s Gary Cahill.
Then Robert Snodgrass, who remains the club’s leading league scorer this season with seven goals, joined West Ham for £10.2m.
Silva took over with the club rooted to the foot of the table and despite six wins in eight home games, the Portuguese failed to mastermind an away win in nine attempts.
