Jurgen Klopp's world champions racked up a 16th consecutive Premier League triumph - and 24th from 25 top-flight games this season - with Salah striking twice in the last 18 minutes.
Alex Oxlade-Chamberlain opened the scoring in the 47th minute against his former club, unleashing a low drive past Alex McCarthy, before Jordan Henderson doubled their lead on the hour mark.
Salah produced a sweet finish for his first in the 72nd minute and showed his composure again at the death to send the Reds 22 points clear of second-place Manchester City, who travel to Tottenham on Sunday.
FULL-TIME Liverpool 4-0 Southampton— Premier League (@premierleague) February 1, 2020
A dominant performance by #PL leaders Liverpool secured all three points at Anfield, with goals from Alex Oxlade-Chamberlain, Jordan Henderson and Mo Salah#LIVSOU pic.twitter.com/aczsjSS4Xe
It took 20 minutes for Liverpool to carve out the game's first opportunity, Salah's effort deflecting narrowly wide off the outstretched leg of Jan Bednarek.
Alisson was alert to paw away Moussa Djenepo's fierce strike shortly before the half-hour mark, while at the other end McCarthy made a double stop to deny Virgil van Dijk's backheel and Roberto Firmino's follow-up.
Danny Ings, Shane Long and Nathan Redmond all had presentable opportunities towards the end of the first half, but they failed to take advantage of uncharacteristic uncertainty in the Liverpool defence.
Ings' penalty appeal after the restart was waved away by referee Kevin Friend, allowing Liverpool to storm up the other end and forge ahead through Oxlade-Chamberlain's low 18-yard drive in the 47th minute.
Salah saw a goal ruled out for offside after 54 minutes, but the Reds pulled further clear when Henderson coolly lifted the ball past McCarthy from 12 yards after being picked out by Firmino's clever cutback.
Salah eventually got on the scoresheet, latching onto Henderson's fine pass and clipping over McCarthy.
He bundled in a fourth from close range in the 90th minute - Firmino supplying his third assist - to add further gloss to yet another win for Klopp's relentless side.
What does it mean? Unstoppable Reds march on after first-half scare
Klopp's side were far from their fluid best during a chaotic first half and were lucky not to be at least a goal down at the interval. Normal service was resumed in the second period, though, and a scarcely believable 16th consecutive Premier League win was essentially wrapped up comfortably.
With such a commanding lead over Pep Guardiola's side, it is surely only a matter of time before they seal a first league title in 30 years.
Henderson at the heart of Liverpool's greatness
England international Henderson has been instrumental in Liverpool's stunning season and he was once again excellent against Southampton. He scored his side's second with a cool finish and created Salah's first goal with an inch-perfect pass.
McCarthy makes it easy for Oxlade-Chamberlain
While the Saints goalkeeper could do little about Liverpool's second and third goals, he was rooted to the spot for Oxlade-Chamberlain's opening strike and might feel he should have done better.
Both sides have FA Cup fourth-round replays in midweek, with Liverpool hosting Shrewsbury Town on Tuesday and Southampton travelling to Tottenham a day later.