Mohamed Salah, the Golden Boot winner last term, scored the only goal of the game midway through the first half to net his second of the new campaign - a precise curling finish from Roberto Firmino's assist.
Firmino had already been superbly denied by Mat Ryan by that stage, but the Australian was not given the thorough examination he might have expected at Anfield.
Jurgen Klopp's men never looked likely to relinquish their lead, however, as Brighton threatened only sporadically, allowing new goalkeeper Alisson and his back four to pick up a third straight clean sheet to kick off 2018-19.
Liverpool began brightly and within 15 minutes had seen Ryan pull off a sensational save to keep out Firmino's downward header and Trent Alexander-Arnold curl a free-kick against the crossbar.
The Reds soon took the lead as James Milner robbed Yves Bissouma high up the field and the ball was worked to the right from Sadio Mane to Firmino to Salah, whose first-time finish glanced in off the far post via Ryan's fingertips.
GOOOOOOAAAAAAAAAALLLLLLLLLLLLLLLLL!!! pic.twitter.com/pYbPmnJenJ— Liverpool FC (@LFC) August 25, 2018
Klopp's men were given a let-off early in the second period as an off-balance Anthony Knockaert shot wide from a promising position inside the box.
There were a couple more nervy moments as the clock ticked down, including Alisson's fine save to keep out Pascal Gross' 89th-minute header, which allowed Liverpool to preserve their status as the only side in the division yet to concede a goal.
What it means: Liverpool the early pace-setters after City slip
The Reds are seen as the likeliest side to challenge dominant defending champions Manchester City, who drew 1-1 at Wolves earlier in the day. A two-point advantage, even at this fledging stage, is undoubtedly welcome for Klopp and his men.
Pat on the back: Fab three provide cutting edge when it counts
Perhaps predictably, Mane, Firmino and Salah were all involved in the decisive moment, linking up to good effect to allow the Egyptian to net his 29th goal in as many Anfield outings.
Boot up the backside: Tough baptism for Bissouma
Perhaps harsh to single out the 21-year-old making his first Premier League start, but it was he who was caught in possession by Milner for Salah's goal as Liverpool executed their trademark high press.
Key Opta stats:
- Of the 17 teams to play in the Premier League both last season and this season, Brighton have won the fewest points in their away games (11).
- Liverpool have kept 11 clean sheets in the Premier League in their 18 games since Virgil van Dijk’s debut in January 2018, more than any other side in that period.
- Under Jurgen Klopp, Roberto Firmino has had a hand in 59 Premier League goals (36 goals, 23 assists), 14 more than any other Liverpool player.
A testing trip to Leicester City next weekend for Liverpool, who have lost three of their last four trips to the King Power Stadium. After a midweek EFL Cup tie with Southampton, Brighton host Fulham on Saturday.