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.
1. Illan Meslier
5 - Distribution let him down badly at times, cleared the ball straight to Henderson for the fourth goal. Made a couple of saves.
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2. Stuart Dallas
5 - Exposed at right-back in the first half but was one of few players to show quality in the second half as a midfielder.
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3. Luke Ayling
4 - Couldn't prevent Liverpool from getting in behind time and time again. Made some last-ditch tackles. Harsh decision against him for the penalty.
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4. Pascal Struijk
4 - Similar story to Ayling. Left with too much to do. Didn't track Matip's run for his goal.
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5. Junior Firpo
4 - Walking a tightrope after his first half yellow. Struggled defensively, couldn't add much going forward.
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6. Adam Forshaw
5 - Battled, showed a nice pass or two but looked overrun in midfield and struggled to stick with his men.
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