Captain Jordan Henderson fired the Reds ahead from 18 yards moments after Alisson had denied Solly March at the other end following Leandro Trossard’s defence-splitting pass.
Yves Bissouma, making his first start since 19 September after recovering from a knee injury, then had an effort tipped on to the post before Sadio Mane headed Liverpool into a 2-0 lead after a cross by Alex Oxlade-Chamberlain, on for the injured Naby Keita.
In an entertaining game, Mane and Mohamed Salah both found the back of the net either side of half-time, but both attempts were ruled out for handball and offside respectively.
In a tense finale, Brighton thought they had won it when Trossard scored in front of The Kop, but it was ruled out for offside.