A mid first-half strike by Mo Salah proved the difference at Anfield as the reds maintained their 100% start to the Premier League.
Following victories over West Ham and Crystal Palace, the reds faced a Brighton side buoyed by last week's victory over Man United.
But on a bright summer's evening on Merseyside, Liverpool showed most of their good work in the first quarter of the game.
Klopp continued with his third consecutive unchanged side - Milner and Wijnaldum keeping out their challengers in midfield and with another impressive performance for the duo, it is hard to see this changing in the immediate future.
In that opening phase of the game Alexander-Arnold saw a free kick hit the crossbar, Sadio Mane went close and Bobby Firmino was denied by the goalkeeping of Mat Ryan when the Brazilian had a headed opportunity at goal.
But Salah's goal was his usual classic. He collected the ball from a Mane pass and curled a left footed shot beyond the reaches of the Brighton keeper. A 29th Salah goal in his 29 Anfield games so far.
After the reds goal, the performance faded somewhat. But as Klopp said after the game: 'Nobody doubts we deserved the three points and that's the important thing,'
In fact, Liverpool might consider the acquisition of Alisson Becker to already be paying dividends. He saved well from a Pascal Gross header late on and showed composure on a number of occasions. Maybe, in a different situation or season, the reds wouldn't have held on to all three points here - in a way that perhaps last week's Crystal Palace game may have turned out differently.
The reds now have a week of rest. Most other Premier League sides are involved in the League Cup 2nd round this midweek, but as European representatives of the league - the reds receive a bye to the 3rd round.
When the Premier League returns, Liverpool travel to Leicester City for the first game of the weekend - a 12:30 lunchtime kick off on Saturday.