Sadio Mane struck twice as Liverpool secured Champions League qualification with a 2-0 win over Crystal Palace at Anfield on Sunday ensuring a third-placed finish for Juergen Klopp's side.
A fifth straight win completed an impressive end to what had been a disappointing and injury-plagued Premier League campaign for last season's champions.
With 10,000 home fans present, Liverpool made a nervy start and Palace's Andros Townsend missed a great chance when he intercepted a poor pass from Trent Alexander-Arnold but with only Alisson Becker to beat, he fired wide of the post.
Liverpool grew into the game though and Rhys Williams should have opened the scoring but, unmarked at a corner, his header flew high over the bar.
Mohamed Salah had an opening but shot straight at keeper Vicente Guaita before Mane broke the deadlock in the 36th minute, firing home from close range after Palace were unable to clear an Andy Robertson corner.
Mane made sure of the win and a top-four spot when he drilled in a left-footed shot in the 74th minute after being set up by Salah.
A run of six defeats in seven games in February and March had threatened to leave Liverpool without a place in Europe's elite competition.
Yet Klopp's side ended the season unbeaten in their final 10 matches, winning eight of them. They finished in third place on 69 points, 17 points behind champions Manchester City.
The game was the final match in charge of Palace for their manager Roy Hodgson, the former England boss who had a brief spell with Liverpool. He is leaving the role at the age of 73.
There were also farewells on the Liverpool side with midfielder Georginio Wijnaldum given a strong send off from the crowd and his team mates. The Dutchman's contract at the club runs out in July and no new deal has been signed.
Liverpool's retiring kitman Graham Carter was also given a guard of honour after the final whistle and was paraded around the field by Klopp.
Chelsea squeeze into Champions League despite defeat at Villa
Chelsea qualified for the Champions League despite losing 2-1 at Aston Villa in the Premier League on Sunday as they pipped Leicester City to a top four spot by one point.
Thomas Tuchel's Chelsea, who had Ben Chilwell on the scoresheet in reply to goals by Bertrand Traore and an Anwar El Ghazi penalty, had to rely on London rivals Tottenham Hotspur who beat Leicester 4-2 away.
Chelsea meet Premier League champions Manchester City in the Champions League final in Porto, Portugal next weekend but wanted to secure their spot in the competition beforehand.
The visitors dominated the first half against Villa, with 68% of possession, but it was their former forward Traore who grabbed the advantage for the home side, hitting the target off the underside of the bar from a Jack Grealish corner.
Chelsea should have equalised through Christian Pulisic before Traore won a penalty in the 51st minute when Jorginho clipped his ankle in the box and brought him down. Dutch midfielder El Ghazi scored from the spot.
Chilwell pulled a goal back for Chelsea in the 70th minute from a Pulisic pass, 10 minutes after Timo Werner had a goal ruled out for offside against captain Cesar Azpilicueta.
Azpilicueta was sent off in the 88th minute after reacting to a Grealish challenge by barging him in the face.
Chelsea started the day in third spot but Liverpool overtook them with a 2-0 home win over Crystal Palace. Chelsea will be concerned for first choice goalkeeper Edouard Mendy who had to be sustituted at halftime after falling heavily into the post.
Pepe sinks Brighton but Arsenal fail to nail Europa Conference League spot
Nicolas Pepe scored twice in the second half as Arsenal beat Brighton & Hove Albion 2-0 in their final Premier League game of the season on Sunday but Mikel Arteta's side failed to qualify for the new Europa Conference League after finishing eighth.
On a frantic final day, Arsenal finished below north London rivals Tottenham Hotspur, who beat Leicester City 4-2 to seal seventh place.
Arsenal dominated possession in the first half and went close to opening the scoring but Rob Holding's goal from a set piece was ruled out for offside while his centre back partner Gabriel saw his floating header come off the crossbar.
Pepe gave Arsenal the lead four minutes after the restart, controlling a low cross from Calum Chambers with his left foot before firing a fierce strike with his right foot past Robert Sanchez in Brighton's goal.
Arsenal doubled the advantage when Martin Odegaard released Pepe down the right channel and the Ivorian forward composed himself to curl a low finish inside the far post for his 10th league goal of the season.
Aguero signs off in style as City celebrate title with Everton rout
Sergio Aguero said goodbye to Manchester City in style as his double off the bench in his final match for the club helped them celebrate the Premier League title in style with a 5-0 thrashing of Everton at the Etihad on Sunday.
Aguero started on the bench as Pep Guardiola named a surprisingly strong starting team given they are playing in the Champions League final next week, but the Argentine could not be held back, helping condemn Everton to a 10th-placed finish.
The already-crowned champions did not take their foot off the gas with little to play for, with Kevin De Bruyne hammering the hosts into an 11th-minute lead, before Gabriel Jesus made it 2-0 three minutes later.
Everton's opportunity to get back into the match came in the 37th minute after Ruben Dias conceded a penalty for a foul on Richarlison, but Gylfi Sigurdsson's spot kick was saved by City goalkeeper Ederson.
After the break, the goals kept coming as Phil Foden finished well to make it 3-0 in the 53rd minute before Aguero took centre stage.
His first goal came after a twisting and turning run in the 71st minute, before a bullet header completed the rout and the perfect afternoon for City and their all-time top goalscorer as the champions finished on 86 points, 12 clear at the summit.
Leicester miss out on top-four finish after loss to Spurs
Leicester City suffered a horrible case of deja vu as their Champions League dream was shattered on the final day of the season for the second straight year after they twice squandered the lead to lose 4-2 at home to Tottenham Hotspur on Sunday.
Jamie Vardy converted two penalties to give Leicester 1-0 and 2-1 leads in the crunch Premier League clash and, with Chelsea losing 2-1 at Aston Villa, that would have been enough for Leicester to claim fourth spot.
But a 76th-minute own goal by keeper Kasper Schmeichel gifted Spurs an equaliser and Gareth Bale, possibly in his last game for Tottenham on loan from Real Madrid, rubbed salt into Leicester's wounds with two well-taken late strikes.
England striker Harry Kane, who could have also been playing his last game for the London club amid transfer speculation, struck Tottenham's first equaliser to take his league tally to 23 this season and win the Golden Boot award.
Just like last term when a Champions League qualifying spot looked to be theirs for the taking, this season's FA Cup winners Leicester finished in fifth place and will have to be content with a Europa League campaign.
Victory left manager-less Tottenham in seventh spot and the minor consolation of a place in the inaugural Europa Conference League -- UEFA's third-tier club competition.
Leicester won the FA Cup for the first time last weekend, but just missing out on a top-four spot, having occupied it for most of the year, was a hammer blow. The Foxes are on 66 points while fourth-placed Chelsea finished with 67 from 38 games.
Vardy opened the scoring in the 18th minute with a calmly taken penalty after VAR correctly awarded the hosts a spot kick after Spurs defender Toby Alderweireld needlessly stuck out a trailing leg to trip the Leicester striker.
Kane levelled in the 41st when he swivelled to volley the ball past Schmeichel from close range.
Vardy restored Leicester's lead from the spot after tangling with Davinson Sanchez as he burst into the area and referee Anthony Taylor gave the penalty.
Again Vardy easily beat Spurs keeper Hugo Lloris and, with news of Chelsea losing at Villa, the 8,000 fans inside the King Power Stadium were in a celebratory mood.
But then everything went wrong.
Schmeichel tried to punch away an inswinging cross in the 76th minute but only managed to divert the ball into his goal.
Ten minutes later Kane was played through and rounded Schemeichel but after the angle became too tight he looked up to pick out the unmarked Bale, on as a substitute, who stroked home with his left foot.
The stuffing was knocked out of Leicester and Bale produced a moment of quality to waltz through the defence before flicking a shot against the post and converting the rebound, taking his total to 14 goals in all competitions for Spurs this season.
It was tough on Leicester who, until losing to Chelsea in midweek, had been in the top four since the start of the year.
McGoldrick strikes to end Sheffield United's season with a win
Relegated Sheffield United bowed out of the Premier League with a 1-0 consolation win over Burnley at Bramall Lane on Sunday, with David McGoldrick's first-half strike enough to separate the sides.
Enda Stevens threaded a pass in the 24th minute to McGoldrick, who sprinted forward into the Burnley half and curled a right-footed shot from outside the box past Will Norris and into the bottom corner.
Paul Heckingbottom's Blades played with tempo and purpose, and had the opportunity to double their lead 10 minutes later when Chris Basham's powerful shot rattled the post.
Burnley lacked any real threat apart from Dwight McNeil and Chris Wood, who drew a handful of good saves from Blades goalkeeper Aaron Ramsdale.
United's seventh win of the season was not enough to lift them off the bottom of the table, and they head down to the Championship with 23 points from 38 games, having lost a whopping 29 times and drawn only twice. Burnley finished 17th with 39 points.
Leeds end superb Premier League season with 3-1 win over West Brom
Rodrigo, Kalvin Phillips and Patrick Bamford all scored as Leeds United ended their season on a high note with a 3-1 win over relegated West Bromwich Albion that helped them to a ninth-placed Premier League finish.
Playing in the top flight in front of their fans for the first time in 17 years, Rodrigo headed home Raphina's corner in the 17th minute to notch his fourth goal in four games and prompt raucous celebrations from the stands.
Phillips scored his first Premier League goal three minutes before the break as keeper Sam Johnstone completely misjudged his free kick into the box, allowing it to bounce past him and into the net.
West Brom almost pulled a goal back in the 54th minute when Matt Phillips hit the post and Leeds midfielder Ezgjan Alioski almost bundled the ball into his own net as he attempted to clear.
Playing their final game for the club, defender Gaetano Berardi and attacking midfielder Pablo Hernandez were given a standing ovation as they were substituted in the 70th minute before Bamford netted his 17th of the season from the penalty spot following a handball by Okay Yokuslu.
Having seen his side waste a slew of chances, Hal Robson-Kanu pounced on a defensive error to score a late consolation goal for West Brom but the Leeds fans refused to allow their party to be spoiled as they celebrated a successful return to the Premier League, finishing with 59 points.
