Carabao specialist Cody Gakpo scored twice - - before the holders held off a late Brighton fightback to reach the last eight.
The Dutch star netted four on the way to winning the trophy last season -and two in the previous round against West Ham. And after a goalless first half at the Amex Stadium, the former PSV forward blew the tie wide open by his sensational opener just 40 seconds after the break.
Gakpo netted a second and Luis Diaz scored a late third as Simon Adingra and Tariq Lamptey netted for the hosts in a frenetic finale. But Arne Slot remains unbeaten in cup competitions at the Anfield club while Brighton have still not got beyond the fourth round of this competition since 1978-79.
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The two sides will play it again in the Premier League at Anfield on Sunday. Both head coaches had made eight changes from 2-2 draws at the weekend, with Andy Robertson given the Liverpool captaincy after his torrid Sunday at Arsenal.
Mats Wieffer, who won the Dutch title playing under Slot at Feyenoord, started for Brigthon. Czech keeper Vitezslav Jaros made an unplanned debut when he came off the bench in the Anfield win over Palace when Alisson Becker suffered a hamstring injury. And the Czech keeper marked his first start with a good early save from Tariq Lamptey when the Ghanaian full-back was sent through by Simon Adringra.
Slot started with Mo Salah and Darwin Nunez on the bench - along with former Brighton favourite Alexis Mac Allister - with Curtis Jones and Dominik Szoboszlai swapping the role of the false nine between the two wide men.
The Hungarian was central to the Reds’ first telling move of the half when he exchanged passes with Robertson before his low shot was saved by the legs of Jason Steele. The Brighton keeper also saved a low Robertson shot with his right boot at his near post.
Gakpo showed how to finish after the break. Playing down the left, first he stepped inside Jakub Moder to smash his right-footed shot into the far corner from the edge of the box. And then he dispossessed Lamptey before beating Steele at his near post low shot after 63 minutes.
In between the two goals, a Brighton counter-attack saw Lamptey cross for Adingra to head back behind Jaros but the Reds keeper outstretched his left hand to tip the ball onto the post. Slot brought on Mo Salah and Darwin Nunez while Fabian Hurzeler threw on Danny Welbeck and Kaoru Mitoma - and the hosts grabbed the next goal.
After 80 minutes, Jarrell Quansah gave away possession deep in his half. Jaros saved a first shot from Ferguson but Adringra poked home the loose ball.
Five minutes later Steele made a save from a deflected Curtis Jones shot before Luiz Diaz beat the Brighton keeper with a low shot. Lamptey ensured a frantic five-minute period of injury time when his 90th-minute shot deflected off Quansah to wrong foot Jaros.
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