Under the management of Arne Slot, Liverpool maintained their winning streak across all competitions, extending Brighton's dismal League Cup record. Brighton has not progressed past this stage since the 1978-79 season.
Both sides made eight changes from the weekend's Premier League fixtures and the opening period lacked quality in the final third. Tariq Lamptey had the best chance when he was denied one-on-one by stand-in goalkeeper Vitezslav Jaros.
But the struggle in front of goal instantly changed within 60 seconds of the second half. Gakpo was allowed to cut inside from the left and fired a rocket into the right corner to put Liverpool in front.
Jaros, on his first Liverpool start, produced a stunning save to tip Simon Adingra's header onto the right post before Evan Ferguson fired over from close range.
TrendingLiverpool then wasted a three-on-one breakaway when Dominik Szoboszlai was denied, but Gakpo doubled their lead seconds later, firing past Jason Steele.
The visitors appeared to be easing into the quarter-finals until Adringra netted from a rebound in the 81st minute although Luis Diaz quickly restored their two-goal advantage by firing in off the post.
There was to be another twist, though, when Lamptey's shot deflected past Jaros in the 90th minute although Liverpool held on.
More to follow.