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.
Marking his return from injury after several weeks out, Kelly was an assured presence on the right side of Liverpool's defence—a welcome piece of news for Kenny Dalglish with the suspension of Martin Skrtel and the continued absence through injury of Glen Johnson.
Kelly was tested by Craig Noone on many occasions, and though the Brighton man got past him and put in the odd cross, Kelly was, by and large, an impressive performer and got forward well when the moment was right.
On the opposite flank, Jack Robinson deserves a mention for an accomplished display, but Kelly just pips him to this fifth spot.
Jay Spearing has been limited to League Cup starts this season, but showed his ability with a steady performance against Brighton.
With Lucas holding, Spearing was able in the first half to get forward and link the play much more than in the past and twice came close to opening his account for Liverpool; most notably with a fierce left-footed drive which was tipped onto the post by the opposing goalkeeper.
His good distribution and workman-like attitude to the game ensured the Reds were rarely overrun in the centre of the park, with almost all Brighton's attacks coming down the flanks.
On another day, Luis Suarez almost certainly would have walked off with the match ball and certainly should have had two goals.
Firstly, he rolled an effort just wide of the far post having sprung the Brighton defence, before he saw a header glance wide off the post with the keeper again beaten.
Suarez was a menace in the first period with his movement and clever link-play, and his contribution to an attacking first period was not to be underestimated.
His partnership with Craig Bellamy showed much promise, and, though he faded out of the game in the second half as Brighton dominated possession, he had another good game in a Reds shirt.
Jamie Carragher didn't have too much to do in the first half, beyond clear a few crosses and set pieces, but in the second half he was a reassuring and commanding presence as Brighton did their best to lay siege to the Reds' goal.
His heading and marking was exemplary, and, as always, his reading of the game was of the highest order. (Several times he was the covering defender as Brighton's wide men looked to exploit gaps in the Reds' defence.)
The only blemish on Carragher's copybook was giving away the late penalty after Spearing lost possession inside the Liverpool box, but even so this was a very good performance from the Liverpool vice-captain—who sportingly gave up the captain's armband when Gerrard made his appearance from the bench.
Man of the match Craig Bellamy served notice of his return to the Red of Liverpool with a virtuoso display that left none in doubt of his best position and commitment to the cause.
His goal was expertly taken with his left foot, finding the far corner with unerring accuracy, but it was his movement and link-up play which impressed the most. Not only centrally, but working the channels, Bellamy was a massive threat in the first half and was Liverpool's main outlet in the second when they relied mostly on counter attacks.
Late in the game it was again his clever movement which led to the second killer goal. Pulling out to the left touchline, he created a huge gap for Maxi and Kuyt to exploit and his pass to the former was well-weighted.
It was a good game against admittedly inferior opposition, but Bellamy has shown he can definitely be considered for first team action in the Premier League.