CARABAO CUP specialist Cody Gakpo scored twice – including a stunning strike into the top corner – 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 with 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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