Leeds United bowed out of the EFL Cup despite an enterprising performance at Anfield as Liverpool marched into the semi-finals 2-0.
Liverpool prodigy Ben Woodburn enhanced his burgeoning reputation by becoming the club's youngest ever goalscorer with a fine finish late on.
The academy graduate, at 17 years and 45 days, beat Michael Owen's record by 98 days to write his name into Anfield history books with an emphatic 81st-minute finish.
Divock Origi scored five minutes before having previously laboured against an industrious Leeds side who took the game to their hosts.
It put Liverpool into a record 17th League Cup semi-final and their fourth in the last six years, having lost the final to Manchester City last season and won the trophy in 2012.
Considering most Premier League teams who come to Anfield now look to suffocate their opponents Leeds manager Garry Monk took the opposite view.
He was rewarded for it as the Sky Bet Championship side dominated the game and the better chances and should have been ahead long before Liverpool finally made the breakthrough.
Hadi Sacko set the tone in only the third minute when he sprang the offside trap only to be denied by Simon Mignolet, one of eight changes from Saturday's win over Sunderland which may have accounted for the lack of rhythm in Liverpool's game.
Aside from Marco Silvestri's save from Georginio Wijnaldum's volley - set up by a sublime defence-splitting pass from 19-year-old Ovie Ejaria - Liverpool barely created anything.
Emre Can almost capitalised on substitute Kalvin Phillips' errant backpass but poked past the far post, and otherwise the Leeds defence were finding it relatively comfortable.
Early in the second half Kemar Roofe, the visitors' chief threat, saw his curling shot rebound off the post after beating Mignolet, who then denied the Leeds attacker's angled shot.
Another chance went begging when Kyle Bartley headed wide at a corner and there was a growing sense that Leeds would pay for missing so many chances against one of the highest-scoring sides in the Premier League.
Wijnaldum crashed a shot against the post before Origi, who had been guilty of wanting too many chances in the penalty area, finally decided to keep it simple and slid in at the near post to convert Trent Alexander-Arnold's cross.
But the biggest roar of the night came nine minutes from time when substitute Woodburn joyously blasted into the roof of the net in front of the Kop to cap a memorable few days for the teenager.
Despite seeing his side exit the competition, Monk was quick to praise his unit.
"The team can be proud of what they did tonight," he said.
"With a little bit more composure, we would have scored two or three goals tonight.
"Unfortunately their quality came through at the end and they scored the goals.
"We deserved more, if we carry on like that we can be successful.
"The ambition now is to have these types of games week in, week out."