United almost got off to a dream start when Stuart Dallas played Hadi Sacko through on goal inside three minutes, but the winger couldn’t get the better of Liverpool goalkeeper Simon Mignolet.
Kemar Roofe then went close with an effort from the edge of the box, again forcing Mignolet into another good save.
Liverpool had a really good chance of their own in the 12th minute, Georginio Wijnaldum was picked out in the area and was only denied by a fine save from Marco Silvestri.
Ragnar Klavan was next to try his luck from the edge of the box, but he was unable to find the target with his effort.
Emre Can then caught Leeds napping at the back, he intercepted a loose back pass, but could only put his effort wide when through on goal.
Kalvin Phillips then came close to a breakthrough just before the break, he saw his deflected effort from the edge of the box go just wide of Mignolet’s post.
Half Time: Liverpool 0-0 Leeds United
Seven minutes into the second period Leeds again came so close to going in front, Phillips stole the ball from Trent Arnold-Alexander on the edge of the Liverpool box allowing Roofe to shoot, but he saw his curling effort come out after hitting the post.
Can then had another chance to break the deadlock, after good play by Lucas, his deflected effort found its way safely into the arms of Silvestri.
Kyle Bartley went close for Leeds at a corner, Taylor delivered, but the central defender saw his header go just wide.
In the 66th minute Leeds had another opportunity, Ronaldo Vieira sent Roofe into the penalty area, but he once again couldn’t get the better of Mignolet who made a good low save.
The hosts took the lead ten minutes later, Alexander-Arnold put in a wicked cross and striker Divock Origi stabbed home.
The Reds doubled their lead in the 81st minute, after some great link up play with a back-heel from Sadio Mane, the ball found its way to Origi, he found Wijnaldum who laid the ball off to 17 year-old Ben Woodburn who smashed home to become Liverpool’s youngest ever goalscorer.
Chris Wood had the ball in the back of the net just two minutes later, following Doukara’s knock down, but the effort was disallowed for offside.
Sacko then had another opportunity six minutes from time, he broke into the penalty area, but could only fire over the bar.
Doukara showed good strength to create an opportunity in the dying minutes, but couldn’t find the target, as Leeds made an exit from the competition, despite a spirited display.
Full Time: Liverpool 2-0 Leeds United
Liverpool: Mignolet, Alexander-Arnold, Lucas, Klavan, Moreno, Stewart (Woodburn 68), Wijnaldum, Can, Ejaria (Milner 83), Mane, Origi (Grujic 90). Subs not used: Karius, Clyne, Lovren, Henderson.
Leeds: Silvestri, Berardi, Cooper (Ayling 46), Bartley, Taylor, Vieira, O’Kane (Phillips 27), Sacko, Dallas (Wood 62), Roofe, Doukara. Subs not used: Green, Grimes, Mowatt, Antonsson.
Booked: Origi (Liverpool), Doukara (Leeds)
Referee: A. Marriner
Venue: Anfield
Attendance: 52,012 (5,352 Leeds)