With the fixtures coming thick and fast, Brighton boss Fabian Hurzeler and Liverpool head Arne Slot both decided to make eight changes to their respective sides.
Liverpool goalkeeper Vitezslav Jaros was among those who were brought into the lineup, and the 23-year-old was forced into early action on his first start for the club, making a strong stop to keep out Tariq Lamptey.
The Reds created their best chance of the first period just after the half-hour mark as Dominik Szoboszlai drew a superb stop out of Jason Steele, before Luis Diaz headed the rebound just wide of the Brighton goal.
They were unable to find the breakthrough before the break, but that soon changed when Gakpo found the net within a minute of the restart.
Gakpo then added a second after stealing possession from Lamptey, before Simon Adingra found the net to give Brighton a lifeline in the 81st minute.
Diaz swiftly restored Liverpool's advantage, only for Lamptey to score in the 90th minute to send up a nervy ending to the contest.
The Reds ultimately stood firm in stoppage time to end Brighton's three-game unbeaten run and send the holders into the quarter-finals.
BRIGHTON VS. LIVERPOOL HIGHLIGHTS
Gakpo goal vs. Brighton (46th min, Brighton 0-1 Liverpool)
Gakpo breaks the deadlock in the first minute of the second period. After collecting the ball on the left flank, the Dutchman cuts inside onto his favoured right foot, before rifling an unstoppable strike past the despairing Steele.
Gakpo goal vs. Brighton (63rd min, Brighton 0-2 Liverpool)
Lamptey makes another mistake just minutes after an error had led to a Liverpool break. Steele made a strong save to bail the right-back out for the previous error, but there was nothing the goalkeeper could do to prevent Gakpo from doubling the advantage. The forward steals the ball from Lamptey, before driving into the box to drill a low strike in at the near post.
Adingra goal vs. Liverpool (81st min, Brighton 1-2 Liverpool)
Brighton have a lifeline. Jarrell Quansah gifts possession to Evan Ferguson, who sees his effort pushed away by Jaros. Adingra quickly pounces on the rebound to prod the ball home to halve the deficit.
Diaz goal vs. Brighton (84th min, Brighton 1-3 Liverpool)
Diaz quickly appears to quash Brighton's hopes of taking the tie to penalties. The Colombia international works the space to fire the ball in at the near post to punish the Seagulls for failing to clear their lines.
Lamptey goal vs. Liverpool (90th min, Brighton 2-3 Liverpool)
Could the comeback still be on? Lamptey lets fly from the edge of the box, and his strike takes a wicked deflection before finding the net.
MAN OF THE MATCH - CODY GAKPO
After fizzing a shot just wide in the first half, Gakpo found his radar in the second period at the Amex Stadium.
The Netherlands international showcased his clinical nature in the final third, producing two unstoppable strikes to put Liverpool in a strong position on the South Coast.
Diaz's late effort may have proved to the decisive goal, but Gakpo was undoubtedly the standout player in the fourth-round tie.
BRIGHTON VS. LIVERPOOL MATCH STATS
Possession: Brighton 45%-55% Liverpool
Shots: Brighton 19-11 Liverpool
Shots on target: Brighton 7-7 Liverpool
Corners: Brighton 6-2 Liverpool
Fouls: Brighton 8-11 Liverpool
BEST STATS
WHAT NEXT?
After suffering EFL Cup disappointment, Brighton will look to avenge this defeat when they travel to Anfield for Saturday's Premier League clash.
As for Liverpool, they will be determined to continue their fine form after winning nine of their last 10 matches in all competitions (D1).