The Reds were able to start goalkeeper Alisson Becker and Fabinho after sitting out the recent FIFA break, but Roberto Firmino missed out because of injury.
The latter's absence didn't matter as Mohamed Salah made the breakthrough on 20 minutes courtesy of a tap-in for his 100th Premier League goal following a ball by Trent Alexander-Arnold.
Leeds were called to switch up their stall with ten minutes to halftime in Pascal Struijk coming on to replace the injured centre-back Diego Llorente.
The Reds didn't stop posing problems a little towards the break and a second seemed on the cards after Sadio Mane worked space for an opening with Harvey Elliott going wide from a rasping shot.
Marcelo Bielsa decided to throw in a substitution right at the restart, with Tyler Roberts brought on to replace former Valencia forward Rodrigo.
It did nothing to prevent the Reds doubling their tally five minutes from resumption as Fabinho slammed home a loose ball off a cutback by Alexander-Arnold after having his initial strike blocked.
Leeds played the rest of the match with ten players inside the last 30 minutes after a tough challenge by Struijk on Elliott brought his dismissal, with Liverpool manager Jurgen Klopp furious.
The numerical disadvantage didn't bother Leeds who looked to cut the deficit from a spectacular strike on the centre line by Patrick Bamford, but Alisson back-tracked to tip away.
Liverpool added a third in time added on when Mane turned from a pass by Thiago Alcantara to beat Illan Meslier with a solid finish and bring the tie to a close.