Liverpool's Egyptian striker #11 Mohamed Salah scores the team's second goal during the English Premier League football match between Liverpool and Brighton and Hove Albion at Anfield in Liverpool, north west England. AFP
The Reds deservedly trailed at half-time to Ferdi Kadioglu's sweet strike at Anfield.
But two quickfire goals from Cody Gakpo and Mohamed Salah punished Brighton for not making more of their first half superiority.
Liverpool's Dutch striker #18 Cody Gakpo vies for the ball with Brighton's Turkish defender #24 Ferdi Kadioglu during the English Premier League football match between Liverpool and Brighton and Hove Albion at Anfield in Liverpool, north west England. AFP
A 13th win in 15 games in charge for Slot takes Liverpool two points clear of Manchester City, who were beaten 2-1 at Bournemouth.
"We were outplayed in the first half," said Slot. "We didn't show up at all.
"The second half the players showed a different attitude and intensity.
"If you face a team like this and are 1-0 down and can come back to a 2-1 win, which in my opinion was deserved, that gives me a lot of confidence. More than the position we are in."
Both sides were much-changed from the League Cup tie between the pair on Wednesday, which Liverpool edged 3-2.
Despite the Reds welcoming back a plethora of stars including Salah, Virgil van Dijk and Trent Alexander-Arnold, it was the Seagulls who dominated the first half and should have been out of sight before the break.
Kadioglu opened the scoring on 14 minutes with a blistering right-footed drive in off the inside of the post.
Liverpool were again without first-choice goalkeeper Alisson Becker due to injury but his stand-in Caoimhin Kelleher produced a vital save to prevent Brighton doubling their lead.
Jack Hinshelwood's sublime pass split the Liverpool defence to set Georginio Rutter in behind Van Dijk, but the Frenchman failed to beat Kelleher.
Kadioglu blazed over another big chance to make it 2-0 before a Danny Welbeck free-kick hit the side-netting.
"Football is always a game of results and we need results, we have to understand how to get results," said a frustrated Brighton boss Fabian Hurzeler after his side slipped to seventh.
"The performance was good enough to in this game easily. If we score the second or third goal the game is completely different."
Liverpool transformed
Liverpool were forced into a change at the interval as Ibrahima Konate hobbled off with his arm in a sling and was replaced by Joe Gomez.
The England defender should have made an instant impact when he headed straight at Verbruggen when unmarked from a free-kick.
Slot's half-time team talk had the desired effect as Liverpool tore out of the blocks a side transformed in the second half.
Alexis Mac Allister's header was turned behind at his near post by Bart Verbruggen before Van Dijk did not connect when picked out by Alexander-Arnold's cross.
Brighton had kept Salah quiet for an hour but the Egyptian should have punished the visitors when he sped onto Darwin Nunez's flick and failed to beat Verbruggen one-on-one.
The home side needed some fortune to get the comeback started as Gakpo's attempted cross flew into the far corner without getting a touch.
With Anfield now in raptures it took just three minutes for Slot's men to find the winner.
From a Rutter fluffed shot at one end, Liverpool broke at speed as Curtis Jones found Salah, who cut inside onto his trusted left foot and smashed into the top corner.
Brighton pushed the hosts back in a nervy finale, but Liverpool held on for a vital three points on a day that title rivals City and Arsenal, who were beaten 1-0 at Newcastle, both stumbled.
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