Hull City's relegation from the Premier League was confirmed on Sunday as they suffered a 4-0 defeat to Crystal Palace at Selhurst Park.
First-half goals from Wilfried Zaha and Christian Benteke, a Luka Milivojevic penalty and a late Patrick van Aanholt strike secured the win for the home side to guarantee their survival, and that of Swansea City, while condemning Hull to a return to the Championship.
Marco Silva's side realistically needed a win to keep their fight to stay up going until the final round of matches, with Swansea's win over Sunderland on Saturday leaving them four points adrift of safety and with a far worse goal difference.
Their hopes took a huge blow after just three minutes, however, as Zaha pounced on Andrea Ranocchia's mistake to put Palace in front, before Benteke's powerful header doubled the lead before the break.
Youngster Jarrod Bowen had a clear chance to grab a lifeline on the hour mark but Wayne Hennessey did not have a save to make in the Palace goal, and Milivojevic's spot-kick and Van Aanholt's close-range effort made certain that Sam Allardyce's record of never being relegated from the top flight remains intact.
Hull, however, will join Middlesbrough and Sunderland in dropping down to the Championship for next season.
Hull kept a first away clean sheet in six attempts in their last game on the road against Southampton, but they found themselves behind with only three minutes played in the sunshine of south London.
Ranocchia swung a foot to clear the ball following a Michael Dawson header but completely missed his kick, allowing Zaha to race into the penalty area and slot the ball confidently beneath Eldin Jakupovic.
Palace spirits were suddenly soaring and James Tomkins nearly made it 2-0 after 10 minutes, nodding the ball narrowly wide after meeting Jason Puncheon's cross from the right at the far post.
Hull appeared not to learn the lesson from that warning, though, and Benteke doubled the lead 11 minutes before half-time after running unchallenged to power a header down and into the net from Puncheon's corner.
15 - Christian Benteke has scored 15 PL goals this season; the most since 2012-13, his debut campaign in English football (19). Mojo.-- OptaJoe (@OptaJoe) May 14, 2017
Puncheon had earlier been fortunate not to concede a penalty after deflecting a Kamil Grosicki free-kick behind for a corner with his hand, and it seemed that luck was firmly against Silva's side when, minutes into the second half, the injured Harry Maguire had to be replaced after Ranocchia and Andy Robertson had already been substituted at half-time.
Bowen was one of those attacking replacements and he missed a golden chance to halve the deficit on 61 minutes, miscuing a half-volley from a Sam Clucas cross from the left with the goal at his mercy at the far post.
The visitors enjoyed 74 per cent of the possession in the second half as Palace dropped deep to preserve their advantage, but they rarely looked likely to add to their meagre total of 36 league goals for the season.
Benteke skewed a promising chance for a third wide but it proved to be of little consequence.
Dawson brought down Jeffrey Schlupp as he raced into the area on the counter-attack, allowing Milivojevic to dispatch the penalty in confident fashion with just five minutes of normal time left.
And as the clock ticked into injury time, James McArthur capitalised on some uncertain defending to slide the ball through to the unmarked Van Aanholt, who slotted the ball beneath Jakupovic as the home fans began to celebrate in earnest.