Arne Slot's side moved eight points clear of second-placed City thanks to Salah's second half double at St Mary's.
After taking the lead through Dominik Szoboszlai's early strike, Liverpool were rocked by Adam Armstrong's equaliser before Mateus Fernandes put bottom of the table Southampton ahead in the second half.
As he has so often done before, Salah came to Liverpool's rescue with a typically predatory equaliser and a coolly converted penalty in the closing stages.
Liverpool's 10th win in 12 league games ensured they capitalised on City's dismal 4-0 defeat against Tottenham 24 hours earlier.
Chasing a first Premier League crown since 2020, the Reds have a golden opportunity to throttle City's hopes of a fifth successive title when Pep Guardiola's team visit Anfield on December 1.
City have lost five in a row in all competitions and Salah said: "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."
Salah now has 12 goals in all competitions this term, including six in his last five league games.
"They were very important, especially after being down 2-1. It's the most important thing to have won the game," he said.
"Each game is different. They had a game plan and played very well. We managed to come back and win the game."
'Urgency and intensity'
Having Salah on form has been crucial to Slot's dream beginning to life at Anfield.
Slot has made a remarkable start, winning 16 of his first 18 games in all competitions.
The former Feyenoord manager's deft touch has established Liverpool as title favourites in his maiden season at Anfield after replacing Jurgen Klopp.
Slot conceded Liverpool lacked intensity in the first hour at St Mary's, but he was pleased with the way his players responded to falling behind.
"In the second half I saw the intensity I was looking for in the first half. Southampton make it really difficult for many teams, including top clubs, and they made it difficult today, though we dominated the game completely in my opinion," Slot said.
"There was not enough urgency to arrive in the box in the first half, we just kept the ball instead of attacking the box.
"Although we fell behind in the second half we showed more urgency and intensity. That led to numerous chances and eventually two goals."
With Salah's contract due to expire at the end of this season and the forward yet to sign a new deal, Slot was quick to praise the contribution of his talisman.
"If you want to win you need to score goals and we know Mo can score," he said.
"For me his first goal is the most important as we scored out of nowhere, then after that it was just waiting for us to score another."
Before City's crucial trip to Anfield next weekend, Liverpool host Real Madrid in the Champions League on Wednesday and Slot is relishing the blockbuster clashes.
"They are two teams who have dominated football the last few years. So two big games and that's why we needed to win today and that is what I am happy about," he said.
