The Liverpool skipper sees action for the first time since March and Spaniard Vicente makes Seagulls debut as Reds make wholesale changes following drubbing at the weekend
Craig Bellamy, who made a return to the starting lineup, grabbed the first goal and Dirk Kuyt sealed the win late in the second half by doubling Liverpool's lead. Ashley Barnes scored Brighton's only goal on a penalty kick in the 90th minute.
With Liverpool not in European football of any kind for the first time since 1999-00 and the Premier League title out of financial reach, the club's focus shifts onto the cup competitions for success this season. The League Cup is a viable option for another addition to the Anfield trophy room.
Dalglish made seven changes from the side which lost to Tottenham on Sunday – although with such a heavy defeat wholesale changes were expected – one of which was bringing Bellamy into the starting XI.
The move paid dividends quickly.
Seven minutes into the game, a marvellous passage of swift, sharp passing from Liverpool allowed Luis Suarez to feed Bellamy. The Welshman strode past the defence to slide the ball into the far post leaving Casper Ankergren floundering. It was the mark of a side with obvious talent and the know-how to implement it.
With Brighton going behind so quickly, the Sussex side receded somewhat fearing a drubbing could be on the cards and this allowed the visitors to dictate the game. Lucas and Jay Spearing in particular were controlling affairs from the heart of the team.
Brighton troubled Liverpool through the second half, but the killer instinct wasn't quite there.
A change was needed by Gus Poyet and what a change he made. Vicente, the former Spanish international who was signed from Valencia in the summer, received rapturous applause when he came on to make his debut for the injured Buckley on the hour.
As time passed the chances of Brighton getting back into the contest waned and Dalglish took this situation to give his captain Gerrard his first competitive action since March when the England man replaced Suarez after 75 mintues.
Liverpool continued to hold the whip hand and Kuyt doubled Liverpool's advantage on 88 minutes with a cool finish to beat Ankergren, who would want to forget this game.
Vicente didn't get on the scoresheet but he did earn the penalty which gave Brighton the slimmest of hopes of a comeback. The Spaniard was felled by Carragher, meaning Barnes stepped up to give the Brighton fans something to cheer.
Liverpool fans would have been pleased with the calm and assured performance and with the knowledge that they are in the hat for the next round which will be drawn this coming Saturday.