Sadio Mane scored twice as Liverpool sealed a third-placed finish and Champions League football with a 2-0 victory over Crystal Palace in front of 10,000 fans at Anfield on the final day of the season.
Liverpool started the final day fourth in the table and knew victory would all-but secure another season in Europe's elite-club competition.
There were nerves early on, as Crystal Palace threatened through Wilfried Zaha and Andros Townsend, and top-four rivals Leicester took the lead against Tottenham to knock the Reds down into fifth spot, but Liverpool roared to an imperious victory.
Mane bundled in his first on 36 minutes as Liverpool took a deserved lead after spurning a host of gilt-edged opportunities and added a second 16 minutes from time to wrap up a vital three points for Jurgen Klopp's side.
The only negative from a Liverpool perspective was that Mohamed Salah failed to get on the scoresheet as he missed out on the Golden Boot to Harry Kane, but that did little to subside the carnival atmosphere inside Anfield, which was tinged with emotion as fan-favourite Georginio Wijnaldum bid the club farewell.
For Roy Hodgson and Crystal Palace, there was to be no fairy-tale ending to his four-year stint at the club as he failed to gate-crash his former employers' top-four hopes in his final game in charge of the Eagles, who ended the campaign in 14th place.
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How Liverpool sealed Champions League football
Liverpool entered the final day finale with destiny in their own hands but were wracked with nerves in the opening exchanges, as Palace threatened to crash their reunion with 10,000 supporters with Anfield.
Wilfried Zaha escaped Nat Phillips with barely four minutes on the clock but was thwarted by Alisson Becker, who produced a fine fingertip save two minutes later to tip Andros Townsend's free-kick from dipping under the Liverpool bar.
Crystal Palace should have taken the lead before the quarter-hour mark when Townsend latched onto Trent Alexander-Arnold's lose pass and raced through on goal, but Liverpool goalkeeper Alisson stood his ground and forced the winger to drill a shot inches wide.
It proved to be a wake-up call for Liverpool, who drew a line under the shaky start and were dominant from there on, but still crucially lacked the final touch.
Alexander-Arnold whistled a free-kick wide as news filtered through that Leicester had taken the lead meaning Liverpool were in danger of missing out on Champions League football. And the mood was not helped by rookie centre-back Rhys Williams missing a sitter when, unmarked, he headed over from six yards.
Salah, attempting to secure his third Golden Boot in four seasons, could not hit the target or beat Vicente Guaita from Thiago's delicious pass. Captain on the day Georginio Wijnaldum took the wrong option in passing to Mane, who curled wide, instead of shooting from Salah's cut-back.
Set-pieces have been Liverpool's weakest area for some time in the absence of the injured Virgil van Dijk but when it mattered most they made one count. Williams atoned for his earlier error by flicking on Andy Robertson's corner and Roberto Firmino's half-control diverted the ball to Mane who poked home from close range, a goal which moved Liverpool into third place.
After Firmino's header was tipped over early in the second half the hosts' tempo dropped, as if they were aware of the situation elsewhere and were just trying to see out time.
It would have been a risky tactic had Palace not been so particularly disinclined to attack and, as a result, Liverpool were able to regain their foothold and deliver the finishing blow.
Fittingly it was started by Thiago, who has finished the season stronger than anyone, who intercepted inside his own penalty area to start a sweeping move which ended with Mane's shot deflecting in off Gary Cahill.
The Golden Boot was obviously preying on Salah's mind by then as twice he opted to shoot with team-mates better placed, but on this occasion his selfishness could be forgiven by fans grateful just to celebrate a top-four finish which looked unlikely only a few weeks ago.
Klopp seals another top-four finish - Match stats
- Liverpool finished the season third, and have now finished in the top four in all five of their full seasons under Jürgen Klopp; it's the club's longest run of finishing as high as fourth in England's top-flight since doing so in 10 straight campaigns from 1981-82 to 1990-91.
- Crystal Palace have lost each of their last eight league meetings with Liverpool, conceding 24 goals in the process (three-per-game on average).
- Liverpool won their two Premier League meetings with Crystal Palace this season by a combined 9-0 score; only against Ipswich in 2001-02 (11-0) have they enjoyed a bigger aggregate margin across two Premier League meetings with an opponent in a season.
What the managers said…
Liverpool manager Jurgen Klopp: "Perfect. It was windy like crazy. It's not good for football. We found a way into the game, scored a great goal. Do you take more risk, or control even more? The second goal was so helpful. I didn't know about other matches.
"I'm so proud of what they've done the last 10 or 15 games and the reaction of the team in bad times. Eight wins out of 10, two draws, that's impressive.
"Energy makes all the difference and we got a lot of energy from outside (the fans). It was not our year for the championship. I'm really happy with third place."
Crystal Palace manager Roy Hodgson: "Now I am pleased it is over, pleased we got through the game without any catastrophe or disasters.
"I know I have to come to terms with the fact my last game has been played and I am now pleased that last game has been played at Anfield, this is one of the temples of football.
"You're in the Premier League to get visits to Old Trafford and Anfield and when I look back on it with a bit more distance I think I will be pleased it was here for the last time, albeit against a team who were much better than us on the day."
Man of the Match - Sadio Mane
Liverpool's Sadio Mane has scored in eight consecutive Premier League games against Crystal Palace, becoming just the second player to score in eight consecutive Premier League appearances against a single opponent, after Robin van Persie against Stoke.
Mane has scored 10+ goals in all seven of his Premier League seasons (2 with Southampton, 5 with Liverpool), the most number of campaigns by any player while scoring 10+ in all of them.
What's next? Euros, transfer window, 2021/22 key dates
Euro 2020 kicks off on Friday June 11 - just 19 days after the conclusion of the 2020/21 Premier League season - and runs until Sunday July 11.
The 2021/22 Premier League campaign will start on the weekend of Saturday August 14 - 34 days after that Euro 2020 final at Wembley.
Clubs will be able to start planning for the new term when the top-flight fixtures are released at 9am on Wednesday, June 16 but transfer business can start in earnest before then, with the summer transfer window opening on Wednesday June 9.
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The 2021/22 Championship season begins a week before the top-flight one on the weekend of Saturday August 7. All Sky Bet EFL fixtures will be announced at 9am on Thursday June 24.