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. Photo by LINDSEY PARNABY/AFP via Getty Images.
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. Photo by Clive Brunskill/Getty Images.
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. Photo by LINDSEY PARNABY/AFP via Getty Images.
4. Pascal Struijk
4 - Similar story to Ayling. Left with too much to do. Didn't track Matip's run for his goal. Photo by George Wood/Getty Images.