Bournemouth's five-year stay in the Premier League is over despite a valiant effort on the final day as their 3-1 victory at Everton was not enough to avoid relegation.
Joshua King's penalty put the Cherries ahead (13) before Moise Kean levelled for Everton with a simple tap-in four minutes before the interval.
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Dominic Solanke restored Bournemouth's lead with a fine header in first-half stoppage time before substitute Junior Stanislas extended the visitors' lead with 10 minutes remaining.
But Aston Villa's 1-1 draw with West Ham ensured there would be no dramatic escape for the south coast club, who return to the Championship.
Bournemouth finish 18th, with one point fewer than Villa, while Everton finish in 12th, the club's worst league finish since 2004.
Everton: Pickford (6), Digne (6), Coleman (6), Branthwaite (6), Keane (6), Gomes (5), Davies (4), Sigurdsson (6), Richarlison (6), Walcott (6), Kean (7).
Subs: Baines (6), Calvert-Lewin (5), Sidibe (6), Bernard (5), Gordon (7).
Bournemouth: Ramsdale (7), Kelly (7), Rico (7), Steve Cook (6), Smith (7), Lerma (7), Gosling (6), Brooks (7), King (8), Solanke (7), Wilson (7).
Subs: Stanislas (8), Wilson (n/a), Billing (6).
Man of the match: Joshua King.
How Bournemouth's fairytale stay ended
"There's been so many great moments within the five years," an emotional Eddie Howe said afterwards. "We really attacked the Premier League and gave it our best shot. It was an incredible ride and an incredible journey, and I include our supporters in that. I feel we were an inspiration for a lot of the clubs from the lower leagues, which is why it's so disappointing to come to this end."
- Howe: This is hardest moment of my career
- Baines announces retirement from football
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- Villa survive after nervy draw at West Ham
There were no fans present with a radio to their ear to relay the message of events taking place elsewhere, but as the whistle blew for the final time on Sunday, there was deafening silence as the Bournemouth players slumped to the ground knowing their fate was sealed.
Howe described his side's task as "difficult but not impossible", highlighting the incredible end to the Championship regular season as a source of inspiration for his players heading into the Premier League's dramatic denouement.
The Cherries finished 14th last season, but since beating Aston Villa on February 1, they have taken just eight points from a possible 39. They avoided a 10th successive away defeat with a performance full of the grit and determination that has been severely lacking throughout the season.
Bournemouth got off to the perfect start when a handball from Richarlison inside the box allowed King to slot home his fifth Premier League goal against the Merseysiders.
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Everton were producing a candidate for "the worst performance since lockdown" according to Jamie Carragher on co-commentary, but they very nearly levelled when Kean found Theo Walcott in space behind the Bournemouth defence but he could only shoot straight at Aaron Ramsdale.
Bournemouth manager Eddie Howe named an attacking line-up. Former Liverpool striker Dominic Solanke came in to join fellow forwards Callum Wilson and Josh King in the starting line-up. Ex-Everton midfielder Dan Gosling returned in midfield at the expense of Philip Billing with a fit-again Adam Smith replacing replacing Jack Stacey.
Everton striker Moise Kean was given his first start since January 21 - the date of his only goal of the season so far - at the expense of the out-of-form Dominic Calvert-Lewin, while Seamus Coleman replaced Djibril Sidibe at right-back, with veteran left-back Leighton Baines on the bench for his last match for the club.
All the energy was with the Cherries' fluid front four, and news of Arsenal extending their lead over doomed Watford would have given them an extra spring in their step - but, against the run of play, the hosts levelled four minutes before the interval.
It was a finely-constructed equaliser as Andre Gomes found Seamus Coleman on the right and, after the Everton captain cut inside Diego Rico, Walcott was allowed to cross first-time for Kean to tap in at the far post.
It felt like a body blow for Howe's men but, as the first half entered stoppage time, Solanke rose to meet Rico's free-kick to glance the visitors back in front. Jefferson Lerma initially claimed the goal having got the initial touch before the ball grazed the former Liverpool striker on its way past the outstretched Jordan Pickford.
Watford began a spirited fightback at Arsenal, but Bournemouth were sticking to their task as Callum Wilson forced a good save from Pickford after a deep clearance down field by Ramsdale was not dealt with by Michael Keane.
The last team to get out of the relegation zone having started in it on the final day were Wigan in 2011, but Bournemouth were still in need of a favour from West Ham.
Everton were horribly lacklustre as Bournemouth came close to extending their lead when Leighton Baines, on his final appearance before announcing his retirement shortly after full-time, produced a superb last-ditch tackle to deny Wilson.
But Bournemouth did find a third as more poor goalkeeping from Pickford allowed Stanislas to take King's pass and fire beneath England's No 1 for his fifth goal in 10 appearances against Everton.
Baines announces retirement
Everton defender Leighton Baines has announced his retirement from football after an 18-year career.
The 35-year-old made 420 appearances for the Toffees having joined from Wigan in 2007 and was capped by England 30 times, appearing at the 2014 World Cup in Brazil.
However, he has played just 17 times in the last two seasons as Lucas Digne took over as first-choice left-back.
Baines was out of contract at the end of the season and, despite the club offering him the chance to extend it by 12 months, he has taken the decision to quit.
News came through of two quickfire goals at the London Stadium, but with ultimately no change to the table as Bournemouth fell just short.
What the managers said
Everton boss Carlo Ancelotti: "I'm grateful to say thank you to Leighton. In the last six months, I've found Leighton to be a fantastic player. I asked him to continue but he decided to stop. I found him a fantastic professional. Everyone is grateful to him but he decided to stop and I respected his decision. I think it was important to us in these six months but he's still a good left-back who is fit and really professional but we have to respect his decision.
"I'm disappointed with the result. I can understand we had less motivation than our opponents but this is not how we wanted to end the season. It's important now for the players to rest as this season was long and complicated. We'll come back in August with new energy and renewed ambition.
"When I lose, I'm always disappointed but the real reason for this defeat was about motivation. The home record is gone, but we must now think about putting together a good home record next season. They had more motivation as they were fighting for the relegation zone. They had a control of the game with the long balls, winning a lot of second balls. We could've been better with the final pass but I thought we built up from the back quite good."
Bournemouth boss Eddie Howe: "I couldn't have asked for any more from my players today. We started on the front foot and it was a very committed performance. We showed a lot of quality at different times. In the second half, Everton came into the game a little bit more and we withstood their pressure.
"I think we showed that when we're on form, we're a very good team today. The emotions are just a lot of pain. I feel very emotional, and I'm trying to keep it together. I feel really sad for the supporters of this club.
"They haven't been here with us for the last part of the journey which has made it even harder. It's a time for reflection and it's a time to see what the next step is.
"I feel very emotional and very disappointed. I feel sad and dejected and I have difficult emotions to feel. I'm very sad for our supporters this evening as they can't be here to share this moment with us.
"With hindsight, there's loads of things you would've done again. Our early performances post lockdown weren't good enough. There are games there that had we performed better then things would've been very different so there's certainly loads to reflect on."
Analysis: Cherries had too much to do
Sky Sports' Jamie Carragher:
"Bournemouth were excellent today. Howe said it was vital that his side made a bright start which is precisely what they did. They had a Callum Wilson chance that was saved by Jordan Pickford, but you could see early on that it was going to be very difficult to stop them today.
"I fancied them to get a result before the game as I don't think there was any side more perfect as opponents for a team fighting to stave off relegation than Everton, and that showed throughout the 90 minutes.
"The performance against Man City recently would've given them the belief and certainly the way they performed today, you're scratching your head with the position they find themselves in. They just left themselves with too much to do and they didn't make a big enough impact when football restarted."
Man of the match - Joshua King
Howe spoke of there being "some incredibly talented players within the squad" - and King will be near the top of the list of players classed as too good to be playing in the Championship next term.
The Norwegian created countless problems for the Everton defence, dispatching his penalty while also holding the ball up for well for his team to build attacks and help secure three points that were in vain.
King has scored 48 Premier League goals for Bournemouth - seven more than any other player.
Bournemouth consigned to relegation - Opta stats
- Bournemouth have been relegated from the Premier League for the first time, ending a run of five seasons in the top-flight.
- Everton lost a home Premier League game for the first time since November against Norwich, with this their first home defeat under manager Carlo Ancelotti.
- Everton finished the season in 12th, their lowest position in the Premier League since finishing 17th in 2003-04.
- Josh King has scored 48 Premier League goals for Bournemouth - seven more than any other player.
- Bournemouth ended a run of nine consecutive away Premier League defeats, with this their first away win since winning 1-0 against Chelsea in December.
- Bournemouth striker Dominic Solanke has scored three goals in his last four Premier League appearances, having found the net just once in his first 59 games in the competition.
The 2020/21 Premier League season kicks off on September 12, and will run until May 23. The EFL has confirmed the Championship season will commence on the same weekend, with their regular seasons ending on the weekend of May 8.
Premier League clubs have voted for the summer transfer window to open the day after the 2019/20 season ends - on Monday July 27 - and run for 10 weeks.