Sadio Mane struck either side of halftime as the Reds registered an eighth win in their final 10 games of the season to finish third in the Premier League.
Jurgen Klopp's men had to celebrate the club's first league triumph for 30 years in an empty stadium last season and their Premier League title defence was blown off course by a series of long-term injuries to key players.
But they avoided the financial hit of missing out on Europe's premier club competition on top of the economic consequences of the pandemic by finding their form in the final months of the season.
When Liverpool beat Palace 7-0 in December, Klopp's men moved five points clear at the top of the table.
Just three wins from their next 14 league games, including six consecutive home defeats for the first time in the club's history, left them languishing down in eighth.
However, Liverpool took 26 points from a possible 30 in their last 10 games to make sure they will be in the Champions League for a fifth consecutive season.
Klopp had urged his players to use the emotion of the return of supporters to Anfield for the first time in 2021.
Before kick-off, there was an emotional rendition of "You'll Never Walk Alone", but the home side started nervously.
Centre-back injuries have been the bedrock of Liverpool's troubles this season.
Virgil van Dijk, Joe Gomez and Joel Matip have all been sidelined for most of the campaign, forcing Klopp to rely on the inexperienced pairing of Nat Phillips and Rhys Williams.
Andros Townsend pounced on hesitation by both Liverpool's centre-backs to intercept Trent Alexander-Arnold's pass, but he fired wide with just Alisson Becker to beat.
Palace had been party poopers at Anfield in the recent past, winning Steven Gerrard's final home game 3-1 in 2015.
However, they could not give departing manager Roy Hodgson a winning send off as Liverpool took control after the first 20 minutes.
Williams somehow headed over when completely unmarked from a corner before Mohamed Salah failed to beat Vicente Guaita.
Salah's goals have kept his side afloat as Mane has by his own admission had the most difficult season of his career.
But the Senegalese got back on the scoresheet when it mattered as he bundled home a corner at the back post on 36 minutes to score for the eighth consecutive game against the Eagles.
The home side were completely dominant after the break and got the breathing space they desired 16 minutes from time when Mane's shot deflected past Vicente Guaita.
Klopp could then afford the luxury of withdrawing Georginio Wijnaldum to a standing ovation of what is expected to be the Dutchman's final Liverpool appearance.
Wijnaldum is out of contract and has been strongly linked with a move to Barcelona.
Guaita denied Salah a share of the Golden Boot with Harry Kane as he turned the Egyptian's effort behind late on.
But Liverpool got the prize they most desired to be competing among Europe's best again next season.
CHELSEA SQUEEZE INTO CHAMPIONS LEAGUE
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 per cent 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 substituted at halftime after falling heavily into the post. (AFP)