Match ends, Derby County 0, Liverpool 3.
Liverpool continued their good recent form by brushing Championship side Derby aside to reach the fourth round of the EFL Cup.
Ragnar Klavan gave the visitors the lead, slotting in his first Reds goal from a Philippe Coutinho corner.
Coutinho got the second after a one-two with Roberto Firmino, before setting up Divock Origi to lash in a third.
Derby offered little throughout, producing only two shots to test keeper Loris Karius on his Liverpool debut.
This was the fourth match the Reds have scored three goals or more this season - and they have netted 19 times in seven games overall.
Even seven changes from Friday's 2-1 Premier League win at Chelsea did not halt their momentum.
One of those players to come in - Estonia defender Klavan - became the club's 10th different goalscorer this season.
In contrast, Derby - struggling in 20th position in the English second tier - have now failed to score in seven of their 11 matches in all competitions this campaign.
Derby manager Nigel Pearson: "I would be first to accept there is a gulf in class tonight, and where we are and where we aspire to be is a considerable difference.
"For us to progress as a club we need to build a squad which can compete anywhere.
"All of the goals had an element of we could have done better, so that is frustrating. Mistakes cost you dearly against sides like this. After that it is damage limitation to make sure it is not an embarrassment."
Liverpool manager Jurgen Klopp: "We were better tonight and we deserved to win, we created plenty of chances. Could we have done better? Yes, but is that important? No.
"You need to be 100% professional in games like this, which could be difficult, but we were ready for every opportunity.
"We could've been better in the first half with the last pass and in the second with our counter attack but we will take 3-0 all day.
"This is a very important tournament for us, for the players, and we have to show it from the first second. Let's go for it."
- 29OlssonSubstituted forLoweat 64'minutes
- 19HughesBooked at 79mins
- 12BairdSubstituted forInceat 45'minutes
- 15JohnsonBooked at 77mins
- 24WeimannSubstituted forElsnikat 55'minutes
- 18MorenoBooked at 45mins
- 14HendersonSubstituted forCanat 57'minutes
- 16GrujicBooked at 76mins
- 11FirminoSubstituted forEjariaat 77'minutes
- 10CoutinhoSubstituted forIngsat 64'minutes
- Graham Scott
- Shots on Target
Second Half ends, Derby County 0, Liverpool 3.
Foul by Alberto Moreno (Liverpool).
Will Hughes (Derby County) wins a free kick in the defensive half.
Foul by Ovie Ejaria (Liverpool).
Timi Max Elsnik (Derby County) wins a free kick on the left wing.
Marko Grujic (Liverpool) wins a free kick in the defensive half.
Foul by Bradley Johnson (Derby County).
Corner, Derby County. Conceded by Marko Grujic.
Attempt blocked. Timi Max Elsnik (Derby County) left footed shot from outside the box is blocked. Assisted by Bradley Johnson.
Attempt missed. Divock Origi (Liverpool) right footed shot from the left side of the box misses to the right. Assisted by Alberto Moreno.
Nathaniel Clyne (Liverpool) wins a free kick in the defensive half.
Foul by Max Lowe (Derby County).
Delay over. They are ready to continue.
Delay in match Divock Origi (Liverpool) because of an injury.
Will Hughes (Derby County) is shown the yellow card.
Attempt missed. Emre Can (Liverpool) right footed shot from outside the box misses to the right. Assisted by Marko Grujic.
Substitution, Liverpool. Ovie Ejaria replaces Roberto Firmino.
Bradley Johnson (Derby County) is shown the yellow card for a bad foul.
Ragnar Klavan (Liverpool) wins a free kick in the defensive half.