The Clarets recovered from a nightmare start to draw 1-1, having conceded to a Neco Williams goal after just two minutes on the clock.
But Scott Parker’s side fought back well and levelled through Jaidon Anthony, who netted for the third time this season already.
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Burnley were the stronger side at the start of the second-half and had chances to edge their noses in front, but were unable to find that killer touch.
Ange Postecoglou’s side ended the game the stronger, but they found Martin Dubravka in inspired form in the Burnley goal.
Here’s how Burnley’s players rated:
Your next Burnley FC read: Jaidon Anthony on Burnley's Liverpool heartache, scoring form and fond Nottingham Forest memories
13. SUB: Zian Flemming - 6/10
For Foster, 86 Gave Foster a deserved rest after another tireless shift, but didn't get much chance to make an impact either way. (Photo by Matt McNulty/Getty Images) Photo: Matt McNulty