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.
13. Tyler Roberts (sub)
4 - A nice turn here and a decent pass there but like his fellow attackers was pretty well marshalled. Photo by George Wood/Getty Images.
14. Joe Gelhardt (sub)
4 - Produced a nice touch early on in his cameo but was marked out of the game and had no real service. Picture by Bruce Rollinson.
15. Michael Oliver (referee)
7 - Had VAR to deal with any controversial moments. Leeds might feel he was a little harsh on them but the referee wasn't the problem. Photo by PAUL ELLIS/AFP via Getty Images.