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.
7. Stuart Dallas
6 - A couple of nice moments in possession but was pulled around the pitch in the first half as Liverpool took control. Picture by Nick Potts/PA Wire.
8. Raphinha
6 - Looked Leeds' best bet of something happening in the final third, especially on the break. Worked tirelessly. Photo by OLI SCARFF/AFP via Getty Images.
9. Jack Harrison
6 - Seemed to improve and grow in influence after the break but still had a moment or two in the first half. Came off when he was playing his best. Photo by Lewis Storey/Getty Images.
10. Rodrigo
4 - Got involved a lot but missed a golden early chance, didn't track Matip for the opener and failed to make the necessary impact. Subbed at the break. Picture by Tony Johnson.
11. Patrick Bamford
7 - Lots of running, just couldn't make a difference with the very few chances that came his way. Audacious effort from long range almost crept in. Photo by OLI SCARFF/AFP via Getty Images.
12. Pascal Struijk (sub)
7 - Defended well and played well up to the red card, which looked harsh on first viewing. The injury to Elliott was awful but there was no malice in the tackle. Photo by Shaun Botterill/Getty Images.