Despite being put on the back foot in the first period, Liverpool managed to break the deadlock in the 44th minute when 18-year-old Lewis Koumas marked his debut with a deflected goal.
Inspired by his teammates maiden senior strike, Jayden Danns came off the bench in the second period to net his first two Liverpool goals and secure his side's place in the FA Cup quarter-final.
While the Reds can look forward to an away meeting with Man United in the last eight, Southampton will now turn their attention back to their bid to earn promotion from the Championship.
Back in action following Sunday's EFL Cup success, a much-changed Liverpool side were forced to negotiate a tricky start against the determined Saints.
Sekou Mara saw his first-minute strike ruled out inside the opening 60 seconds, before Kamaldeen Sulemana sent his curling effort against the upright.
Caoimhin Kelleher was then required to deny Mara on a couple of occasions to ensure the scoreline remained goalless.
Although the Southampton chances became less frequent, the visitors still managed to carve through the Liverpool defence in the 37th minute when Kamaldeen drove purposely into the box, only to fire straight at the resolute Kelleher.
As the first half near its conclusion, Harvey Elliott tried his luck from range with his fierce strike drawing a strong save from Joe Lumeley.
Just moments later, Koumas found a way past the Southampton goalkeeper, with his low strike finding the bottom corner with the help of a deflection off Jan Bednarek.
Russell Martin's side continued to create and spurn chances after the restart as Kamaldeen saw his near-post effort kept out by Kelleher, before an unmarked Shea Charles drove his shot into the side netting after the ball kindly dropped to him from a corner.
The Saints were ultimately made to rue those missed opportunities when Danns came off the bench to mark his third senior appearance with a brace.
More to follow.