The Reds were in control for most of the match and the scoreline exemplified their dominance. They found the net with all three of their shots on target, starting with Firmino's low drive in the penultimate minute of the first-half.
Phillips then doubled their advantage early on after the break with a bullet header for his first Liverpool goal before substitute Oxlade-Chamberlain put the icing on the cake with a third.
From being on the periphery of qualifying for European football to all but securing a place in the Champions League, Jurgen Klopp's side have turned it around in style in the last couple of weeks. They now close out their campaign at home to Crystal Palace on Sunday.
Here are the player ratings for Liverpool:
Alisson - 7/10
Even though most of the action happened at his opposite end, there were moments where Alisson's interventions were needed, and he did just alright. Another clean sheet to his name too.
Trent Alexander-Arnold - 7/10
The marauding right-back was a constant outlet for Liverpool and kept the Clarets on his toes. However, Alexander-Arnold again came up short defensively, with Charlie Taylor setting up shops in the space provided by him.
Nathaniel Phillips - 7.5/10
He often came up against Chris Wood but won the battle against him. Phillips even opened his account for Liverpool with a perfectly-placed header and stole the show with an off-the-line clearance.
Rhys Williams - 6/10
The weakest link in Liverpool's defense as Williams looked shaky and was caught out quite often. His best moment of the night came early on when he produced a superb block on Matthew Lowton.
Andrew Robertson - 8/10
Robertson looked like his old self again, ripping Burnley's defense to shreds and laying two assists on the night too. He's peaking just in time for the Euros.
Thiago Alcantara - 6/10
One of the few disappointments on an otherwise brilliant night for Liverpool as Alcantara missed a big chance in the first-half and couldn't produce anything meaningful on the ball either.
Fabinho - 7/10
A solid performance from the Brazilian as he gave Burnley's attackers a tough night and read the game brilliantly. He made five clearances and won two aerial duels to deny them from set-pieces.
Georginio Wijnaldum - 6.5/10
Much better from the Dutchman, who's seemed more like a spent force this season. He held his ground well and remarkably completed 100% of his passes.
Mohamed Salah - 6.5/10
The Egyptian ace was uncharacteristically sloppy in the attack, wasting a few good chances to put Liverpool in front before fading in the final quarter of the match.
Roberto Firmino - 8/10
Where was this version of Firmino all season? He followed-up his amazing brace at Old Trafford with another goal tonight which set Liverpool on their way.
Sadio Mane - 7/10
The Senegalese winger was involved in Liverpool's first two goals, brilliantly tracking Robertson's run for the first before beating Gudmundsson to set up their second.
Alex Oxlade-Chamberlain - 7/10
A decent cameo from the Liverpool midfielder who capped it off with a fine strike in the 88th minute.
James Milner - N/A
He replaced Wijnaldum a minute before Oxlade-Chamberlain's goal but cut an anonymous figure.
Kostas Tsimikas - N/A
The Greek star came on to just see out the final few seconds of the match.
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