They struggled to recover from gifting Wilfried Zaha a third-minute goal, and will return to the Sky Bet Championship next season after this defeat left them four points from safety with only one fixture to play.
Palace had needed only a draw to preserve their Premier League status but effectively secured victory with Christian Benteke's 17th goal of a largely difficult season
Luka Milivojevic and Patrick van Aanholt added further finishes, while the result also secured Swansea's Premier League status.
Palace manager Sam Allardyce had spoken during the week of the need for his team to handle the pressure of the occasion and of how the opening goal would be key
He also recognised the potential for the Selhurst Park crowd to grow nervous, but if either team had displayed a lack of composure, it was Hull.
Scarcely two minutes had passed when the erratic Italian defender Andrea Ranocchia's missed kick allowed Zaha directly through on goal, and from there the winger calmly finished beneath goalkeeper Eldin Jakupovic
As with Swansea's 2-0 victory at Sunderland on Saturday, it already appeared that by taking the lead the hardest part was done, and after a quiet period of play the home side added a second in the 34th minute.
Jason Puncheon targeted Benteke with his inswinging, right-wing delivery and the Belgian's powerful header, under minimal supervision from the Hull defence, had the beating of Jakupovic
From that point on Hull - who had rallied since the appointment of Marco Silva as manager in January - had the air of a defeated team
Palace had no reason to play with ambition, knowing their visitors required a minimum of two goals, and defended with the organisation Allardyce has given them.
The Eagles continued to threaten on the counter-attack and the third goal was scored from the penalty spot by Milivojevic with five minutes left after Dawson tripped Jeffrey Schlupp in the box.
The final blow to Silva's side came in the last minute as James McArthur's through-ball sent fellow substitute Van Aanholt clear to calmly place a shot beneath Jakupovic
Hull, who will finish 18th, had begun the season with only 13 fit senior players, without a permanent manager and amid widespread predictions of relegation
Silva's contract expires at the end of the season, and it would seem that keeping him on board represents Hull's best chance of making an instant return to the top flight
Source : PA