Marco Silva's side slipped to a 4-0 defeat at Selhurst Park that ensured they will return to the Championship after only one season back in the top flight.
Goals from Wilfried Zaha, Christian Benteke, Luka Milivojevic and Patrick van Aanholt secured the victory and guaranteed Palace's survival under manager Sam Allardyce.
To make matters worse for Hull, Michael Dawson's foul on Jeffrey Schlupp with five minutes of normal time left saw them concede a penalty for the 13th time this term – a record for a club in a single Premier League campaign in England.
13 - Hull have conceded 13 penalties this season, more than any other side in a single Premier League campaign. Nightmare.— OptaJoe (@OptaJoe) May 14, 2017
Milivojevic converted before Van Aanholt ensured another milestone was met in south London, with his 90th-minute goal the 1,000th scored in the Premier League in 2016-17.