Alexander Isak scored for a third straight Premier League game as Liverpool inflicted only Brighton's second loss of the season.
Isak's goal, finished emphatically from Bradley Barcola's right-wing cut-back, came four first-half minutes after Pascal Gross had diverted a Florian Wirtz shot into his own net.
Brighton arrived at Anfield having scored 23 goals in their first seven games of the season but lacked a clinical edge, with Yasin Ayari blazing a golden chance over moments before the opener.
Ayari later struck the post with a curling effort from outside the box as Brighton finished the game with only one shot on target despite having 64 per cent of the possession.
Trey Nyoni, a second-half substitute for Wirtz, who went down the tunnel after taking a knock to his ankle, also made a crucial, last-ditch tackle to deny Maxim De Cuyper in the Liverpool box.
The hosts had chances to add to their lead, wasting several counter-attacks and drawing Bart Verbruggen saves from Ronald Araujo and Cody Gakpo. But their first-half flurry proved sufficient to secure a first Premier League home win under Andoni Iraola.
The result takes them above Chelsea into fourth in the Premier League, only a point behind Brighton, who taste defeat for the first time since August. Liverpool's fourth win in a row in all competitions also provides further evidence of their attack finally clicking.
Isak's goal, his sixth of the season in the Premier League, came after fine work by summer signing Barcola, who stole possession high up the pitch before driving forward and picking out his team-mate.
Momentum is building for Liverpool under Iraola. It's four wins in a row now and eight in 10 going back to the start of September.
They had to ride their luck at times. Brighton should have been in front before their opener. But the hosts were rewarded for attacking quickly and directly, in the style of their head coach.
Liverpool won possession in the final third five times - their second-highest total in the Premier League this season. Iraola values speed and incisiveness above possession, so the fact they had a meagre share of the ball is unlikely to concern him.
Instead, he will take satisfaction from the contributions of his attacking players. Barcola provided an assist for a second straight Premier League game, this time having been swapped to the right flank. Isak led the line with another clinical display.
Wirtz had bright moments too, taking the shot that forced the opening goal before coming off in the second half, while Rio Ngumoha, their star man in the midweek win over Villarreal, was only needed for a quarter of an hour with Gakpo also impressing.
Liverpool head coach Andoni Iraola speaking to Your Site:
"Very happy. We needed this win at home and to celebrate with the supporters. A really good performance.
"We started really aggressively and needed this start because we had been coming from behind lately. Especially against a team full of confidence like Brighton, we were very focused on starting well, scoring first and, luckily for us, we did it.
"This is the fourth win in a row, it feels good. We have to keep going, we still have points to recover but I'm liking a lot of things.
"Good performances from the players, they are helping each other, we are playing together with collectiveness. Some of the players will have better or worse performances, but today it was a team that you can trust."
On Wirtz's injury: "He had to leave the pitch with a small twist of the ankle. It doesn't look very big but we're playing every three days so we have to see what it is.
"I don't know if it is even an injury. He twisted his ankle and it's painful in the moment and he didn't feel 100 per cent. We decided to put on Trey and he played a good performance."
Brighton head coach Fabian Hurzeler speaking to Your Site:
"It was a missed opportunity.
"Everyone felt we could definitely take something away from this game. We came here to play our way. We made two easy mistakes to give them a present to score two goals.
"We had plenty of chances to score. We kept trying. They defended well in the box and have individual quality. We did everything. We have to avoid easy mistakes. We had chances but didn't have luck on our side today.
"We had a big chance with Yasin. If that goes in, the game is completely different. We have to learn we don't have to chase the game.
"We lost our structure a little bit at 2-0 down. We wanted to come back as quickly as possible and lost our structure. That's what we have to analyse and do better.
"In the second half, and also a lot of phases in the first-half, only one team was playing and trying to win."
