Jurgen Klopp’s men finished runners-up in the competition last season and return to Anfield needing to overturn a 1-0 loss to the side they have raided for key players in recent years.
Redmond’s first-half strike was the difference at a packed-out St Mary’s, bringing a timely end to Southampton’s four-match winless run in all competitions on their first appearance in the last four of a major competition since 2003.
Claude Puel’s men rallied after a sluggish start against the side second in the Premier League, with Redmond capitalising on Ragnar Klavan’s mistake to slot home.
Unfortunately for Saints, Redmond did not show the same cutting edge with his two other first-half opportunities, while Cedric’s decision to shoot rather than cross after the break may return to haunt them.
Redmond saw an effort hit the underside of the bar as the hosts attempted to add a deserved second, but they will have to make do with just a one-goal advantage in the return leg at Anfield on 25 January.
Southampton looked to be in for a bleak evening as they struggled in the opening stages, defending deeply and struggling to find an attacking outlet.
Liverpool were exposing the full-backs with ease as Puel’s team started nervily, but Fraser Forster denied Roberto Firmino when the visitors eventually managed to turn that dominance into a clear-cut chance.
Jay Rodriguez was looking overwhelmed as Saints’ focal point, yet there was a flash of life in the 19th minute as Redmond collected a cross from the right and got away a shot that Loris Karius smothered well.
Redmond was caught out by the goalkeeper’s reactions, but made amends within a minute as Klavan’s inability to deal with a simple ball forwards cost his side.
Rodriguez was alert to capitalise on the hashed clearance, beating former team-mate Dejan Lovren with a deft pass to put Redmond through and this time the 22-year-old did not falter, keeping his composure to direct past Karius.
That sucker-punch, after such a comfortable start, threw Liverpool off kilter, failing to attack with any intensity before half-time.
Southampton, instead, ended the opening period on top. Jordy Clasie saw an audacious attempt comfortably dealt with by Karius, who was a match for Redmond’s close-range effort after collecting a Dusan Tadic cross just before the break.
The Serbian, signed as Adam Lallana’s replacement in 2014, saw a threatening cross-shot cleared soon after play resumed, with Southampton pressing well and frustrating the Reds.
Daniel Sturridge’s claim that he was upended in the box was ignored by referee Neil Swarbrick and Firmino saw a long-range effort stopped with ease, before Klopp, pictured, turned to star man Philippe Coutinho.
Out since 26 November with an ankle injury, the Brazilian returned as a 61st-minute substitute in a bid to inspire the visiting side.
Coutinho was soon thrilling the raucous travelling support with his skill in winning a corner, but Saints broke at speed when that set-piece came to nothing and looked set to score, only for right-back Cedric to try his luck rather than cross.
In the longer run, the introduction of Coutinho was unable to inject much sustained attacking impetus to struggling Liverpool.
Saints continued to look the bigger danger and, after Rodriguez had an effort saved, substitute Shane Long beat Lucas Leiva on the left. Redmond met Long’s low cross with a chipped effort that beat Karius but not the crossbar, with Lovren clearing on its way down.