Jurgen Klopp’s men finished runners-up in the competition last season and need to overturn a first-leg 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.
Yet midfielder Redmond was left to rue his missed chances despite scoring the goal which put Southampton in the driving seat.
“I should have had four today; on another day they might go in. We got the win in the first leg so we take it on to the second leg,” said Redmond.
When asked which missed scoring opportunities he regretted the most, he said: “The first one and the last one. The last one I tried to be a bit too smart and just chip it over. I’ll take those mistakes and try to put it right in training and the next game.
“We got a clean sheet and a win in the first leg so we’ll take that on to the second.
“It’s credit to the whole team, we’ve got to work hard for each other and we did that today.”
Saints’ captain against Liverpool, Virgil van Dijk, was satisfied after keeping a clean sheet. “We won today and kept the clean sheet which is the most important thing,” he said.
“We played some good football at times. Obviously Liverpool are a great team. We were good on the ball as well. It was a great team performance today.
“It’s all about communication. They have a lot of movement up front and a lot of running so we really talked to each other and I think we did it really well and it’s a good win to go to Anfield.”
Liverpool boss Klopp admitted his side should have performed better, but with the return leg at Anfield still to come, thinks everything is still to play for.
“We lost timing,” said the German. “We weren’t compact enough. We can do much better.
“It was open and open games are difficult. Loris (Karius) had to save us a few times. It’s only half-time so all good.
“We should have been more clear in our passing. Everything is (still) possible for us so it’s OK.
“Tonight we were not good enough over the whole 90 minutes but we can do better and nobody should think it’s already decided.”
Claude Puel’s men rallied manfully after a sluggish start against the side second in the Premier League, with Redmond capitalising on Ragnar Klavan’s mistake to coolly slot home.
Unfortunately for Saints the England U21 international 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 January 25.
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 nervously, 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 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 hacked 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 turned to star man Philippe Coutinho.
Out since November 26 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, substitute Shane Long beat Lucas Leiva on the left. Redmond met his low cross with a chipped effort that beat Karius but not the crossbar, with Lovren clearing on its way down.
Sturridge and Coutinho blazed over at the other end in a desperate attempt to level, but they were unable to cancel out Southampton’s advantage.
Forster, Cedric, Yoshida, van Dijk, Bertrand, Clasie (Hojbjerg 74), Romeu, Davis (Ward-Prowse 82), Redmond, Rodriguez (Long 82), Tadic.
Stephens, McQueen, Sims, Lewis.
Karius, Clyne, Lovren, Klavan, Milner, Wijnaldum (Coutinho 61), Lucas, Can, Lallana, Sturridge, Firmino (Origi 83).
Gomez, Moreno, Mignolet, Stewart, Woodburn.
Neil Swarbrick (Lancashire).