Darwin Nunez set Liverpool on the path to victory over Southampton as Arne Slot’s side reached the Carabao Cup semi-finals.
First-half strikes from Nunez and Harvey Elliott gave Liverpool firm control, although Cameron Archer pulled a goal back to give the hosts hope.
Southampton were led by interim manager Simon Rusk following the sacking of Russell Martin after Sunday’s 5-0 home defeat by Tottenham, and they started brightly but fell behind after 25 minutes.
Trent Alexander-Arnold did superbly to escape pressure from two Southampton attackers before finding Nunez with a through ball, albeit via a huge deflection off Jan Bednarek. The Uruguay international took advantage of Alex McCarthy’s slip to place his finish out of the goalkeeper’s reach.
Any hopes Southampton fans had that cup duty would distract from their struggles at the foot of the Premier League evaporated when Elliott doubled Liverpool’s lead eight minutes later.
The England Under-21 midfielder – making his first start of the season – sent a shot into the bottom left corner via a deflection after Cody Gakpo played him in on goal.
Slot – sitting in the stands while serving a one-game touchline ban – must have felt the game was going comfortably Liverpool’s way as the visitors withdrew Alexander-Arnold and Joe Gomez at half-time in favour of Konstantinos Tsimikas and Federico Chiesa.
Liverpool eased off and paid the price just before the hour mark when Archer collected the ball, ran half the length of the pitch virtually unchallenged and curled a stunning strike into the far corner of Caoimhin Kelleher’s goal.
Southampton grew in confidence but had Taylor Harwood-Bellis to thank for clearing Chiesa’s goal-bound effort, and while they fashioned a few promising attacks none of them led to an equaliser.
They wanted a penalty in the final minutes of injury time, but referee Simon Hooper judged Jarell Quansah did not drag down Mateus Fernandes when through on goal.
Last season’s cup winners join Arsenal and Newcastle in the semi-finals, as will one of Tottenham or Manchester United who face off in the final last-eight tie on Thursday (20:00 GMT).