Bournemouth's five-year stay in the Premier League came to an end despite beating Everton at Goodison Park as Aston Villa's draw at West Ham meant they were relegated to the Championship.
The Cherries needed a win, and for Watford and Aston Villa to both lose against Arsenal and the Hammers respectively, if they were to retain their top-flight status.
The Hornets lost 3-2, but a 1-1 draw for Aston Villa ensured survival for Dean Smith's side.
It was a disappointing outcome for Bournemouth, who had done all they could in their game to give them hope of staying up.
Eddie Howe's side looked determined to fight for their survival right from the outset and deservedly went ahead when Joshua King scored from the penalty spot after Richarlison handled inside the area.
Bournemouth could have had a second penalty soon afterwards for a handball by Lucas Digne but neither the referee or the video assistant referee felt there was an infringement.
Despite all their dominance, the visitors conceded an equaliser as half-time approached when Moise Kean tapped in Theo Walcott's cross.
But Bournemouth restored their lead just before the break as Dominic Solanke headed in from Diego Rico's delivery.
The second half was nervy affair as the Cherries looked to hold onto their slender lead, but they grabbed a third and much-needed breathing space in the final 10 minutes after Jordan Pickford let a tame Junior Stanislas shot slip under his gloves and into the back of the net.
The visitors had done all they could to ensure survival, meaning all eyes were on events at West Ham, but a point was enough to keep Aston Villa in the top flight at Bournemouth's expense as Howe's side finished 18th.
Reaction to the final day of the Premier LeagueCherries show fight, but ultimately too late
Bournemouth's players walked off the pitch at full time with their heads bowed in disappointment as news came through that a crucial result elsewhere had gone against them.
It was a bitter blow for the visitors after putting in a battling display at Goodison Park, but ultimately they paid the price for failing to show similar fight in previous games this season.
A promising start to 2019-20, in which they lost only three of their first 11 games, proved to be a false dawn. But their form nosedived and a run of 19 defeats in their last 25 games meant they plummeted into trouble.
Injuries have not helped Bournemouth's cause, with the likes of Charlie Daniels, Joshua King, David Brooks, Nathan Ake and Callum Wilson having had significant spells on the sidelines.
But the disappointing form of players who have been available did not help. Ryan Fraser provided 14 assists in 2018-19 - only Eden Hazard managed more - but was a shadow of his former self this season and has not played since the restart after rejecting a short-term extension to his expiring contract.
Meanwhile, big-money signings Solanke and Jordan Ibe, who was released this summer, ultimately failed to deliver.
Solanke and his team-mates all stepped up on the final day of the season to give Bournemouth a chance - they were first to every ball in a determined first-half display and looked much more like the Bournemouth of previous seasons.
But ultimately that show of fight came too little, too late as they now contemplate a first Championship campaign since 2014-15.
Toffees fail to impress as season fizzles out
It was hard to read too much into this performance from an Everton side that were largely going through the motions.
Their season had effectively ended some weeks ago and they could not finish higher than 11th, even if they had managed to beat Bournemouth.
But the Toffees' display will still have been disappointing to Everton fans, who were perhaps hoping they would show signs that they could develop into a team that could fight for a top-six finish next season.
Kean was handed a chance to impress Carlo Ancelotti as he made his first start since 21 January and he repaid his manager's faith with a goal and an overall positive display, with the striker one of the few home players willing to chase down lost causes and make attacking runs.
Jarrad Branthwaite, Everton's 18-year-old defender, started for the second game in a row and once again did not look out of place, but too many other players put in distinctly average performances.
The defeat meant Everton finished 12th - their lowest placing at the end of a season in 16 years - and Ancelotti knows plenty of work will need to be done over the summer if he is to get the Toffees challenging higher up the table.
Man of the match - Diego Rico (Bournemouth)
'We haven't been good enough' - what they said
Everton manager Carlo Ancelotti: "It is a performance that we could expect, it was the last game of the season and the motivation was not so strong. We are not happy, but we have to look forward. The players need rest, it was a busy season and we will come back with more ambition.
"Sometimes the motivation makes the difference on the pitch. Moise Kean did well, he is young and has to improve but it is important that he could score."
Bournemouth manager Eddie Howe on BBC Radio 5 Live: "We were excellent today, the frustrating thing when you see us play like that and you wonder where it was throughout the season.
"Over a 38-game period we haven't been good enough, I'm not going to sit here and complain about how other teams got their points. When you see how we played today, that is a side that should have got more than 38 points."