The Reds' U21s made it four consecutive league victories with the result on Friday night.
A Kieran Morrison penalty in the sixth minute proved the decider for Rob Page's team.
See the key moments of the game in the video above.
Watch U21s highlights: Brighton & Hove Albion 0-1 Liverpool
Watch extended highlights of Liverpool's 1-0 win at Brighton & Hove Albion in Premier League 2.
