However, they had little to celebrate as the Reds strengthened their hopes of a top four finish with a 3-0 win.
Jurgen Klopp's side are now in a strong position to qualify for next season's Champions League after avenging their defeat at Anfield earlier in the campaign.
Roberto Firmino sent them on their way when finishing Andy Robertson's cross on the stroke of half-time.
Nat Phillips settled the nerves when heading home from Sadio Mane's delivery in the 52nd minute.
And substitute Alex Oxlade-Chamberlain rounded things off when beating Will Norris at his near post on the goalkeeper's Premier League debut for the club.
The Clarets have now gone 10 games without a win at home in the top flight.
1. Will Norris 5.9
Handed his first Premier League start. Might have done better to prevent Firmino's opener from passing and beaten at his near post by substitute Oxlade-Chamberlain for the third.
2. Matt Lowton 6.8
His diagonals from right back posed issues for Liverpool's centre-back pairing, who had their work cut out with Wood. Battled well with Mane, who resorted to theatrics when things didn't go his way. Saw a first half drive blocked by Williams.
3. Charlie Taylor 7
Did well defensively up against Salah and had the beating of Alexander-Arnold when bombing forward. Looks after the ball remarkably well and, more often than not, is a key outlet for the Clarets. Another good display.
4. James Tarkowski 7.2
Shut the door a number of times when Liverpool looked to create space inside the box. Made an excellent block to prevent Mane's effort from reaching the target in the first half and made an equally impressive intervention to deny Salah after the break.