A late penalty from Ashley Barnes was not enough to prevent the Reds from continuing their path along their first domestic cup run under Kenny Dalglish since he re-joined the club in the second half of last season.
A convincing first-half display should have been enough to see Liverpool through comfortably, but they only had Bellamy's goal thanks to a first 45 minutes which saw a Kuyt effort cleared off the line, a Luis Suarez effort roll just past the post and a succession of chances hit the post and bar. (First a Suarez header, then a long-range Bellamy free-kick and finally a Jay Spearing effort from the edge of the box.)
In the second half Brighton pushed the Reds back more as they searched for an equalizer, but Kuyt's break-away goal near the end of the game all but finished the tie before a late Barnes consolation penalty meant a nervous last few minutes.
Steven Gerrard made his return from injury after six months out with a 15-minute appearance from the bench, while Martin Kelly also returned, playing 85 minutes before Jon Flanagan replaced him.
Elsewhere there were starts in midfield for Spearing and Maxi Rodriguez, while Sebastian Coates made his full debut for the club and Bellamy made his first start since returning to Liverpool.
Here are the Reds' top five performers from the game.