Mohamed Salah got the only goal of the game as Liverpool made it three wins from three at the start of the new Premier League season, but Brighton produced a gutsy performance and could have stolen a point late on to follow on from their famous 3-2 win over Manchester United last time out.
Liverpool withstood the late pressure to maintain their record of being the only team yet to concede this season though, taking full advantage of Manchester City's earlier slip-up at Wolverhampton Wanderers to gain an early march on the champions in the title race.
It did not take long for Liverpool to gain control of the match, and their first chance arrived after only five minutes when Sadio Mane released Salah before continuing his run into the box to meet the return pass, only to place his finish narrowly wide of the target.
Brighton responded with a chance of their own when Anthony Knockaert cut inside before drawing a routine stop from Alisson Becker, but that was as close as the visitors came in a first half which saw them surrender the lion's share of possession.
Liverpool should have taken the lead in the ninth minute when Andrew Robertson swung a dangerous cross into the middle which Roberto Firmino met with a firm downward header, but the Brazilian was denied a first goal of the season by a stunning reaction stop from Mathew Ryan.
It felt like only a matter of time before Liverpool would break the deadlock, though, and they came closer still moments later when Trent Alexander-Arnold thundered a free kick against the crossbar after Naby Keita had been brought down on the edge of the box.
The breakthrough finally arrived midway through the first half when James Milner stole possession off full debutant Yves Bissouma deep inside the Brighton half before Mane and Firmino combined to find Salah, who passed a pinpoint finish across goal and into the bottom corner for his 29th goal in as many appearances at Anfield.
Brighton boss Chris Hughton will have been unhappy with the manner of the goal, but he could have few complaints at seeing his side fall behind and it almost got worse shortly after the half-hour mark when Georginio Wijnaldum stung the palms of Ryan from a tight angle.
Moments later Robertson whipped a devilish ball into the box which Mane turned goalwards without knowing too much about it, and Firmino also threatened with a shot which flew over the crossbar shortly before half time.
Brighton avoided any further damage, though, and almost produced a smash-and-grab equaliser in the opening stages of the second half when good work from Glenn Murray saw the ball end up at the feet of Knockaert, who snatched at his effort and sliced it off target.
It hinted at a half in which complacency began to creep into Liverpool's game as the tempo of their play dropped, although it was the hosts who continued to look the most likely to get the game's second goal.
Joe Gomez planted a header straight at the keeper shortly after the hour mark, while Firmino also tested Ryan and Shane Duffy almost turned the ball into his own net when trying to cut out Robertson's low cross from the right.
As long as the deficit remained one, Brighton still had belief that they could steal a point from the game, and the increasingly sloppy hosts provided them with one or two reasons for encouragement as the Seagulls' pressure began to grow in the final 10 minutes.
Clear chances were still at a premium for the visitors, though, and Liverpool could have put the game to bed once and for all when Alexander-Arnold saw his deflected effort bounce narrowly wide after good work from Milner and Robertson.
Salah's resulting corner was met by Wijnaldum with a Gianfranco Zola-esque flick at the near post, but a mixture of Duffy and Murray scrambled the ball away before it came straight back at them, with Salah firing high and wide after finding some rare space.
Brighton's big moment came in the 89th minute when Pascal Gross - brought on as a sub less than 10 minutes previously - stole between two defenders to plant a header towards goal, only to see Alisson palm his effort away.
It proved to be the visitors' last sight of goal as Liverpool ground out the win to continue their perfect start to the season, leaving them top of the table with three wins from three and no goals conceded.
Indeed, the Reds have now kept four clean sheets on the bounce for the first time since May 2017 and have still not conceded at home in the Premier League since February - their best run since a nine-game streak under Rafael Benitez in 2007.
Brighton, meanwhile are still winless on the road in the Premier League since November, although rarely in that run of 15 games without victory will they have taken as much encouragement from defeat as they will from today's match.
LIVERPOOL (4-3-3): Alisson; Alexander-Arnold (Matip 89'), Gomez, Van Dijk, Robertson; Milner, Wijnaldum, Keita (Henderson 67'); Salah, Firmino, Mane (Sturridge 80')
BRIGHTON (4-5-1): Ryan; Montoya, Duffy, Balogun, Bong; Knockaert (Jahanbakhsh 76'), Propper, Stephens, Bissouma (Gross 80'), March (Locadia 75'); Murray