Meanwhile, Manchester United only required a point to beat Sunday’s opponents Leicester to a Champions League spot, but a 2-0 win delivered a third-placed finish. Chelsea won by the same scoreline against Wolves to take fourth.
Villa survive on a tense final day at the bottom
Three teams began the day fighting for one survival spot. Aston Villa, Watford and Bournemouth were separated by just three points and with almost identical goal differences as they scrambled to avoid joining Norwich City in next season’s Championship.
It was Villa who had their fate in their own hands, with a 1-0 win over Arsenal on Tuesday taking them out of the bottom three on goal difference from Watford, with Bournemouth three points behind them.
The Cherries began the day favourites for the drop but goals from Joshua King, Dominic Solanke and Junior Stanislas gave them hope at Goodison Park.
Pierre-Emerick Aubameyang’s double and Kieran Tierney’s goal condemned Watford to relegation, despite Troy Deeney and Danny Welbeck pulling them back into contention.
Villa looked to be staying up in style as Jack Grealish scored an 84th-minute opener at London Stadium but Andriy Yarmolenko scored one minute later to ensure a tense finish that paved the way for celebrations at the final whistle.
312 consecutive days in the top four – but Leicester miss out
With champions Liverpool and runners-up Manchester City having already booked their places in next season’s Champions League, it was left to Manchester United, Chelsea and Leicester to battle for the final two places in Europe’s elite club competition.
Manchester United began the day in pole position in third, aware avoiding defeat at fifth-placed Leicester would be enough to secure a top-four finish. Chelsea, meanwhile, required just a point at home to Wolves.
Bruno Fernandes converted from the penalty spot for visitors United after 71 minutes and Jesse Lingard sealed their 2-0 victory in injury time.
At Stamford Bridge, two goals in first-half injury time, from Mason Mount and Olivier Giroud, ensured FA Cup finalists Chelsea a win that knocked Wolves out of the guaranteed Europa League places.
Wolves began the day in sixth but Tottenham climbed above them on goal difference with a draw at Crystal Palace, where Harry Kane’s goal was cancelled out by Jeffrey Schlupp.
What else happened?
Results: Newcastle 1-3 Liverpool, Manchester City 5-0 Norwich, Southampton 3-1 Sheffield United, Burnley 1-2 Brighton
Manchester City’s thumping 5-0 victory over relegated Norwich prevented champions Liverpool from setting a new record for the biggest Premier League title-winning points margin and handed goalkeeper Ederson the Golden Glove award for the most clean sheets.
Liverpool came from behind to defeat Newcastle as Virgil van Dijk, Divock Origi and Sadio Mane overturned Dwight Gayle’s first-minute goal. The champions finish 18 points clear of Pep Guardiola’s side, who still hold the record for the largest top-flight winning margin, having ended the 2017-18 campaign 19 points ahead of runners-up Manchester United.
Kevin de Bruyne scored twice – and also equalled Thierry Henry’s long-held record for the most assists in a single Premier League season – with goals too for Gabriel Jesus, Raheem Sterling and Riyad Mahrez.
The Premier League bade a fond farewell to Manchester City legend David Silva, making his 309th and final English top-flight appearance, after helping the club win 11 major trophies in 10 years.
Elsewhere, Danny Ings scored an 84th-minute penalty to finish the season one goal behind Golden Boot winner Vardy – and level on 22 goals with Arsenal’s Aubameyang – as Southampton beat Sheffield United 3-1.
Che Adams scored twice after John Lundstram’s opener for Chris Wilder’s side, who finished ninth following an excellent first campaign back in the English top flight.
Burnley’s Nick Pope had hoped to secure at least a share of the Golden Glove with Ederson, but his chances of a 16th league clean sheet of the season were ended after 20 minutes against Brighton, by Yves Bissouma’s excellent long-range strike.
Chris Wood equalised for Burnley, who were already guaranteed a top-half finish, but Aaron Connolly made it 2-1 for the visitors, who finish seven points clear of the bottom three.