Joel Matip's 30th-minute strike and a pair of Mo Salah penalty conversions gave Liverpool a three-goal lead at half-time.
The hosts kept a firm grip on the game although Marcelo Bielsa's men looked to have stemmed the flow of goals before a Sadio Mane brace and a bullet Virgil Van Dijk header in the final ten minutes heaped further pain on the Whites.
As part of a miserable evening for the Elland Road outfit, Burnley also recorded a 1-0 victory at home to Tottenham Hotspur to leave Marcelo Belsa's side just three points clear of the drop zone and the 18th-placed Clarets have two games in hand.
Graham Smyth, the YEP's chief football writer, hands out the scores from a night to forget for Leeds at Anfield.
7. Mateusz Klich
4 - Got about the pitch but largely chased shadows. Couldn't produce much in the way of link-up play. Withdrawn at the break. Photo by Clive Brunskill/Getty Images.
8. Rodrigo
4 - A couple of nice moments aside he was unable to offer the quality or composure Leeds needed in possession. Photo by PAUL ELLIS/AFP via Getty Images.
9. Raphinha
3 - Arguably his worst showing for Leeds. Nothing went right for him at all. Composure and end product deserted him throughout. Photo by PAUL ELLIS/AFP via Getty Images.
10. Jack Harrison
4 - Tried to get down the flank and create. Should have had an assist for Leeds' big first half chance. Photo by Clive Brunskill/Getty Images.
11. Dan James
4 - Ran lots, chased shadows lots. Almost robbed Alisson in a big first half moment. Could do little else. Service to him was poor. Photo by Clive Brunskill/Getty Images.
12. Jamie Shackleton (sub)
4 - Was willing, put in plenty of effort but couldn't prevent Liverpool from attacking so effectively on his flank. Photo by Stu Forster/Getty Images.