The Merseyside giants travelled down to the South Coast knowing that victory would take them eight points clear of Manchester City at the top of the table after the champions' shock 4-0 home loss at the hands of Tottenham Hotspur.
Liverpool's quest for success at St Mary's started off well, as Dominik Szoboszlai capitalised on a defensive error from Russell Martin's men to draw first blood, but Slot's side were lackadaisical and lethargic at times.
The Reds were punished for such uninspiring play when Adam Armstrong tapped home the rebound from his saved penalty, before teeing up Mateus Fernandes to give the hosts the lead at the start of the second period.
However, another piece of questionable goalkeeping from Alex McCarthy allowed Mohamed Salah to prod home the equaliser, before the Egypt international netted his 100th away goal in a Liverpool kit from 12 yards to complete a terrific turnaround.
Slot matches Carlo Ancelotti, Guus Hiddink feat
Liverpool's victory was their 10th in just 12 Premier League games this season, and Slot has now matched the record for the fewest amount of games a manager has taken to win 10 Premier League matches.
Guus Hiddink and Carlo Ancelotti also needed just 12 matches to earn 10 Premier League victories during their time in charge of Chelsea, with the former's only aberrations in his opening 13 matches being a draw with Everton and a loss to Tottenham Hotspur.
After Hiddink vacated the Chelsea chair to Ancelotti in 2009, the now-Real Madrid boss won 12 of his first 14 matches in the top flight, only being beaten by Wigan Athletic and Aston Villa in that sequence.
Sunday's five-goal spectacular was also a momentous day for Salah, who registered his 100th goal on the road for the Merseyside giants, and the Egyptian now boasts an exceptional 10 goals and six assists from 12 Premier League matches in 2023-24.
However, even though the Reds have now increased their insurmountable lead at the top of the table, Salah is refusing to get carried away, warning that a wounded Man City are capable of flipping a switch at any point.
Salah issues Man City warning before Premier League clash
"They were very important, especially after being down 2-1. It's the most important thing to have won the game," the former Chelsea attacker told Sky Sports at full time.
"Each game is different. They had a game plan and played very well. We managed to come back and win the game. I think we have a good game plan, we played our game and I was confident we would create chances.
"It's great. Hopefully, we keep going in that direction. We have a game against them so hopefully, we win it and go 11 points clear. Man City is Man City. They have a bad time now but they have great players."
Liverpool's next Premier League game comes against none other than Man City at Anfield next Sunday, but before that mouthwatering battle, the Reds have the small matter of a Champions League blockbuster against Real Madrid to navigate on Wednesday.