Roberto Firmino gave the visitors the lead after just six minutes, but Saints steadied the ship to resist Liverpool's early aggression.
However, Southampton's best intentions were thwarted shortly before half-time, with Mohamed Salah firing home after an outstanding move with Firmino.
The hosts were fatigued in the second half as they attempted to fight their way back, but Liverpool remained composed to collect the win and move into third above Tottenham Hotspur.
Both teams provided their lineups before kick-off, as Liverpool's Virgil van Dijk returned to his former club after his recent transfer to Anfield:
Saints started nervously in the opening moments, and Liverpool swarmed as they attempted to take an early advantage.
The Reds' endeavour was immediately rewarded as a counter-attack ended with a goal, with Salah assisting Firmino for the quick opener.
It appeared to be an ominous start for Saints, as Liverpool coach Jurgen Klopp celebrated on the touchline.
Firmino's form as a striker this term has been incredible:
The goal should have set the Reds off to a big victory, but Southampton reorganised as they pushed forward for an equaliser.
James Ward-Prowse was dangerous as he attempted to pick the lock of Klopp's team, and Van Dijk was tested as he organised the defence.
However, Liverpool continued to plug away and doubled their advantage three minutes before the interval.
Salah linked beautifully with Firmino on the edge of the box, and the lethal Egyptian fired the ball past goalkeeper Alex McCarthy.
The second half failed to live up to the excitement of the first, and Klopp's men kept an iron grip on the result.
Saints appeared weary in the challenge and didn't have enough in the tank to mount a credible comeback.
Klopp will be delighted with what he witnessed, and his team leapfrog Spurs in the table as they chase United.
The Reds are now only two points behind the Red Devils after their 1-0 defeat at Newcastle United on Sunday, and the race for places in next season's UEFA Champions League is heating up.