Jurgen Klopp rang the changes and despite a few nice flashes of quality, the Reds struggled to gel in the first half in front of an expectant Anfield crowd.
The visitors in contrast clearly enjoyed the opportunity of taking on a Premier League side, as both Kemar Roofe and Hadi Sacko went close.
Leeds continued to push after the break, with Roofe hitting the post with a curling effort but they could not take their chances and eventually paid when Divock Origi opened the scoring on 76 minutes after good work on the right by Trent Alexander-Arnold.
Garry Monk's side went further behind five minutes later when Ben Woodburn grabbed his first senior goal, in the process succeeding Michael Owen as the club's youngest ever scorer.
Leeds thought they had got one back shortly afterwards, only for Chris Wood's strike to be disallowed for offside.
In the end it was a case of what might have been for the Whites, as Liverpool booked their place in the semi-finals for the third year in a row.