Liverpool went ahead in the 20th minute when Mo Salah poked home Trent Alexander-Arnold's cutback and Alexander-Arnold's corner set up the Reds second for Fabinho five minutes after the break.
Leeds had lost Diego Llorente to injury in the first half and his replacement Pascal Struijk was then sent off on the hour mark after being given a straight red card for a challenge on Harvey Ellliott, despite winning the ball.
United kept looking to respond and Patrick Bamford almost scored with a spectacular lob from the halfway line but the Reds added a third in second half stoppage time via Sadio Mane.
Graham Smyth, the YEP's chief football writer, hands out the scores.
13. Tyler Roberts (sub)
6 - Some good movement but couldn't make a telling impact. Missed the one good chance that was presented to him. Photo by Shaun Botterill/Getty Images.
14. Daniel James (sub)
6 - A couple of bright moments. Looked unsure of what was required out of possession, given he's trained so little with Leeds. Photo by Laurence Griffiths/Getty Images.
15. Craig Pawson (referee)
5 - Let some things go that looked free-kick worthy and gave free-kicks for others that weren't. The red card was controversial. Photo by Paul Ellis - Pool/Getty Images.