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.
1. Illan Meslier
7 - Some good distribution, some not so good. A couple of smart stops.
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2. Luke Ayling
5 - Not up to the standards he set last season. A couple of vital defensive interventions in the second half.
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3. Liam Cooper
6 - Unable to get to grips with van Dijk in the air at set-pieces, struggled with some of Liverpool's movement. Defended bravely when down to 10.
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4. Diego Llorente
7 - Looked up for it, defended aggressively and played some nice stuff. The injury was desperately unfortunate.
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5. Junior Firpo
4 - Struggled badly with the one v one defensive side in the first half. Leeds looked fragile on the left.
Picture by Jonathan Gawthorpe.
6. Kalvin Phillips
9 - Superb. His passing was magnificent, showed his full range. Made interceptions, tackles and blocks.
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