Mohamed Salah made the difference once again at Anfield as Liverpool went to the top of the Premier League for the first time in nearly two years.
Salah, who scored 44 times in an outstanding debut season following his move from Roma, struck midway through the first half to maintain his goal-a-game record on his home ground.
It left Jurgen Klopp's men on top of the pack with maximum points and the last team in the division yet to concede a goal.
Mo Salah's lone strike delighted Anfield fans
In a tight first period, Brighton's Yves Bissouma was robbed of the ball inside his own half, allowing Salah to eventually finish a slick move.
Liverpool were a long way short of their best and didn't create many chances in the second period as a result. Brighton's best opening came late on when Pascal Gross headed straight at Alisson Becker from close range.
After his remarkable debut season for Liverpool, all eyes have been on Salah at the start of this campaign to see whether he could repeat his goalscoring feats. The signs are good for the Egyptian early on.
The forward showed tremendous composure to fire the Reds ahead, taking Roberto Firmino's pass into his stride perfectly and stroking a pass into the bottom corner.
It was a goal that delighted the home supporters.