Arne Slot had to watch from the stands as Darwin Nunez gave the Reds the lead in the first half, though he was no doubt helped by the poor wet conditions that impacted goalkeeper Alex McCarthy.
Harvey Elliott doubled the lead with his first goal of the season to give the visitors a commanding advantage heading into the half-time interval.
Southampton pulled one back in the second half after Cameron Archer brilliantly capitalised on Wataru Endo's mistake in possession, but despite pushing for an equaliser, the Saints could not find a second.
The visitors have progressed to the semi-finals alongside Arsenal and Newcastle United, and will await the outcome of Tottenham Hotspur's match against Manchester United on Thursday before they find out their opponents in the next round.
SPORTS MOLE'S VERDICT
Some had suggested that Liverpool should prioritise their Premier League campaign given they are best positioned to capitalise on Manchester City's weaknesses, but Slot must take the EFL Cup seriously considering his side are just one round away from Wembley.
Perhaps Slot will be most pleased that his players rarely had to exert themselves, and with a game in the Premier League against Tottenham Hotspur to come on Sunday, the Reds should have plenty left in the tank.
Liverpool have won the EFL Cup 10 times - more than any other team - and though the Reds will face another Premier League side in a two-legged semi-final, Slot must feel confident that he can earn his first trophy as manager at Anfield.
Jurgen Klopp reached the final of competition in his first season in charge of the Merseysiders, and it would be a remarkable achievement if Slot was able to do one better.
Liverpool will face one of Arsenal, Newcastle United, Manchester United or Tottenham in the semi-final, but the Reds would likely be considered favourites regardless of who they draw.
SOUTHAMPTON VS. LIVERPOOL HIGHLIGHTS
Darwin Nunez goal vs. Southampton (24th min, Southampton 0-1 Liverpool)
Trent Alexander-Arnold plays a long pass through the middle, but Jan Bednarek's poor clearance allows Darwin Nunez to race through unopposed to goalkeeper Alex McCarthy, who slips and is unable to recover before Nunez slots home from close range.
Great composure from the striker!
Harvey Elliott goal vs. Southampton (32nd min, Southampton 0-2 Liverpool)
Wataru Endo and Cody Gakpo combine with short passes in the middle before the latter finds Harvey Elliott on the right of the box, and the Englishman takes the ball into the penalty area before striking into the bottom-left corner via a deflection.
Two shots on target from Liverpool, two goals!
Cameron Archer goal vs. Southampton (59th min, Southampton 1-2 Liverpool)
Endo gives possession away near the halfway line and Southampton drive forward through Cameron Archer, who carries the ball into the right side of the penalty area before curling an effort into the right of the net.
MAN OF THE MATCH - HARVEY ELLIOTT
Harvey Elliott started his first game of the season, and he showcased his immense ability in the final third after collecting the ball and scoring Liverpool's second goal of the game.
The attacker allowed the likes of Endo and Joe Gomez to fire balls between Southampton's defensive lines, assured that Elliott would keep possession in congested areas.
Elliott was also a threat during counter-attacks, as while he was not able to carry the ball forward at pace, he always looked to play quickly to players such as Nunez, and the Englishman was instrumental to almost all of the Reds' attacks.
SOUTHAMPTON VS. LIVERPOOL MATCH STATS
Possession: Southampton 31%-69% Liverpool
Shots: Southampton 6-14 Liverpool
Shots on target: Southampton 4-4 Liverpool
Corners: Southampton 3-7 Liverpool
Fouls: Southampton 10-10 Liverpool
BEST STATS
WHAT NEXT?
Southampton take on Fulham at Craven Cottage in the Premier League on Sunday before they face West Ham United on December 26.
As for Liverpool, they will hope to collect six points from their next two league fixtures, the first of which comes against Tottenham Hotspur away from home on Sunday, and the second against Leicester City next Thursday.
Written by
Lewis Nolan