Jurgen Klopp's side fought back from a goal down to take all three points, after Danny Welbeck had fired Brighton into a second-minute lead.
Luis Diaz equalised for the Reds midway through the first half, before Mohamed Salah fired home what turned out to be the winner with 25 minutes remaining.
The win takes Liverpool three points clear of Arsenal, ahead of the Gunners' clash with Manchester City at the Etihad later today.
Coming from behind to win means Liverpool have won yet more points from losing positions, moving clear in that metric with 26 over the course of this season.
For Brighton, they remain down in ninth, one point off Newcastle in eighth, which could be enough for European qualification this term, but Roberto De Zerbi will be slightly disappointed at his team's lack of threat in the second half.
With much of the attention being placed on today's later kickoff, Liverpool were fancied by many to get the job done here ahead of that heavyweight clash between Arsenal and Man City.
However, Anfield was stunned inside 90 seconds, when Virgil van Dijk failed to clear under pressure from Jakub Moder, and the ball sat up perfectly for Welbeck, who unleashed an unstoppable strike beyond Caoimhin Kelleher in the Liverpool goal.
Liverpool soon found their feet though, and began an onslaught on the Brighton goal, with Salah culpable of missing numerous first-half chances.
It was Salah who provided the assist for Diaz's equaliser on 27 minutes though, heading the ball back into the danger after a corner was cleared, and Joel Veltman failed to make proper contact on the ball, inadvertently setting up the Colombian to prod past Bart Verbruggen.
Brighton looked rejuvenated following the goal though, and had much joy down the Liverpool right against Conor Bradley.
Simon Adingra ran riot on the young full-back for the rest of the first half, as he, Welbeck and Moder all went close for the visitors.
Darwin Nunez was unfortunate towards the end of the opening 45 minutes with an opportunistic effort while on the floor, which bounced off Verbruggen to safety for Brighton, as the sides went in level at half time.
The hosts continued their territorial domination after the break, as both Alexis Mac Allister and Salah saw headed chances go begging from close range within 60 seconds of each other.
Nunez then went close again shortly after the hour-mark, but the home crowd did not need to wait long for the goal that would put them in front.
Some fine footwork from Mac Allister on the edge of the area opened up the space for him to play Salah through, and with his ninth shot of the game, the Egyptian finally found the back of the net, putting Liverpool in front with a fine left-footed finish.
The Anfield support were on their feet again just minutes later, when Salah's inch-perfect through ball found Diaz, who managed to squeeze his effort through the legs of Verbruggen and into the Brighton goal, before being denied by the linesman's offside flag in a devilishly tight call which was confirmed by VAR.
Brighton gained some momentum late on, as Lewis Dunk saw two headed efforts spilled by Kelleher, but the Liverpool goalkeeper was unpunished for his slightly untidy handling.
Adam Lallana almost spoiled the day against his former club, but could only drag his effort wide, and a few more attempts from Salah went begging in injury time, but Liverpool ultimately ran out victorious.