The first half was goalless in Brighton when Liverpool came to visit.
However, it was close to the home team taking the lead already after eight minutes, when Solly March's finish went past Alisson in the goal.
But Trent Alexander-Arnold threw himself forward and was able to stop the ball from crossing the goal line at the last second.
But after the break, March got at least revenge for the failed attempt.
He gave his Brighton the lead early in the second half.
Karou Mitoma delivered the ball in front of goal and March was able to poke it in from close range.
March victory director
It was then the same March who made it 2-0 on the board, with a left-footed finish, just minutes after his first goal of the match.
A couple of sharp chances, and four substitutions, followed for Liverpool without getting a hole in Brighton.
Instead, substitute Danny Welbeck scored 3-0, played in by March.
Brighton's left winger was thus behind all three goals in the match, which ended 3-0.
It is Liverpool's second straight loss, after 3-1 against Brentford last time.
The result also means that Brighton passes Liverpool in the table, to seventh place.