Liverpool had started brightly but they fell behind in the 20th minute when Redmond found the bottom corner of the net after being set up by Jay Rodriguez.
They should have extended their lead as Liverpool produced one of their worst displays of the campaign, but both teams will go into the second leg at Anfield with all still to play for.
Read below to see how the action unfolded at St Mary's.
6.46pmHello, and welcome to Sports Mole's live coverage of the match in the EFL Cup semi-finals between Southampton and Liverpool.
6.49pmLast night, we witnessed Manchester United make relatively light work of Hull City in the first leg of their tie at Old Trafford but this evening, we should see a much closer contest between Southampton and Liverpool, who will both believe that they have a great chance of reaching the final of this competition next month. The EFL Cup is often seen as a distraction but when you reach this stage of the competition, it becomes a primary focus as a match at Wembley Stadium becomes a realistic possibility.
6.53pmBoth clubs also have different ambitions this season. For Liverpool, it's all about finishing in the top four of the Premier League table and even making an assault on the title, while Southampton will now be targeting seventh place after losing ground on the teams above them. They are realistically too far away the likes of Manchester United and the clubs above so their campaign revolves around the EFL Cup, the FA Cup and putting a run together in the league. Claude Puel will be aware that there can be no slip-ups this evening.
6.54pmAnyway, without further ado, let's crack on with the team news which is emerging at St Mary's.
7.00pmFirst of all, let's take a look at Southampton as Puel names a very strong team, as expected. Nathan Redmond, Jay Rodriguez and Dusan Tadic form a three-way attack, while Steven Davis gets the nod alongside Oriol Romeu and Jordy Clasie. The defence is as expected, too, with Jose Fonte being left out again after handing in a transfer request.
7.04pmAs for Liverpool, Jurgen Klopp also selects his strongest possible outfield lineup with Daniel Sturridge getting the nod of Divock Origi in attack. Loris Karius is preferred in goal to Simon Mignolet, while there is a notable inclusion on the bench as Philippe Coutinho finally makes his return to the first-team squad after initially being penciled in for an appearance in the team on New Year's Eve. He could make his first appearance since suffering an ankle injury in November.
7.09pmHEAD TO HEAD! Tonight's fixture represents the 104th time in which these two teams have met in a competitive fixture, with Liverpool winning on 51 occasions compared to the 28 victories for the Saints. Since 2013, there has been a wide range of results ranging from Saints scoring three in home victories to Liverpool netting six on their travels but Southampton do have just one triumph from the last seven contests.
7.13pmIt has been less than two months since the teams last met at St Mary's. However, on that occasion, a goalless draw was played out, with Southampton being more satisfied with a point than their free-scoring rivals. It was in sharp contrast to the previous two games which had been staged on the south coast...
7.19pmIn March, Liverpool opened up a two-goal advantage over their hosts but they were stunned during the final 26 minutes of the match as Southampton pulled off a famous win. Click here to have a read back on that match.
It was a different story when the two sides clashed during the early stages of this competition last year. Southampton took a very early lead but they were left having to deal with a demoralising defeat. Click here to see how Liverpool ran riot on that occasion.
7.22pmWe mentioned that Manchester United faced Hull City last night and ran out relatively convincing winners. In the event that you didn't follow that match, feel free to click here and have a read back on what proved to be a good evening for Jose Mourinho's team.
7.27pmDaniel Sturridge has struggled for goals in the Premier League this season but that hasn't been the case in the EFL Cup. The England international has netted doubles against both Burton Albion and Tottenham Hotspur and he heads into this game as the top goalscorer in the competition. He also has found memories of this ground having scored at St Mary's three times during the last campaign so don't be surprised to see the 27-year-old make an impact tonight.
7.31pmScoring goals has proven to be a problem for Southampton all season but it will be their usually-reliable defence which Claude Puel will be worried about tonight. Before Christmas, they had the third best defensive record in the Premier League but in their last four games in all competitions, they have conceded 11 goals, six of which have come at home. They have also only won one of their last four games at St Mary's so they cannot be feeling all that confident heading into this match.
7.35pmPREDICTION! Despite the differences in form, we are backing this to be a close match. Southampton are in need of a big performance and they need to show signs of solidarity if their season is not to peter out. However, Liverpool are full of quality in the final third and we are backing either Coutinho or Origi to net a late winner after coming off the bench. Liverpool to win 2-1.
7.38pmBefore we get going, a quick reminder that this is just the first leg. The two teams are scheduled to square off for a second time at Anfield at the end of the month.
7.44pmThe two teams have made their way out onto the pitch at St Mary's. We will be underway very shortly.
4 minSouthampton began strongly by sending a couple of crosses into the Liverpool penalty area but the visitors responded with an assault on the Saints goal with the defence having to out-muscle Can.
6 minThere's a decent pace to this match. Both teams are looking to go on the offensive and while there have been no chances to speak of, it certainly hasn't been for the lack of trying.
9 minLiverpool hold onto the ball for at least two minutes before Firmino is dispossessed cheaply around 30 yards from goal. What a waste of time. Southampton kick the ball into touch soon after they win it back.
12 minMoments ago, there was a bit of concern over Van Dijk, who seemed to jar his back when challenging for a high ball. He was down for a several seconds but he hasn't required treatment. Southampton can't afford to lose their leader in this game.
15 minWe are still awaiting the first shot at St Mary's. Liverpool are making all of the running but they haven't really come close to creating an opening. Lucas and Can are seeing a lot of the ball in the middle of the park.
18 minCHANCE! Unsurprisingly, the first real chance falls to the visitors and it involves Lallana heading the ball back to Firmino who is standing around 16 yards out. He wastes no time in getting a volley on goal but Forster is able to tip the ball over the crossbar.
19 minCHANCE! Karius gets his fair of stick but he does brilliantly to get out well to block from Redmond, who had looked to direct the ball into the far corner at the back post.
20 minSouthampton have rallied over the last couple of minutes and they get their reward with the first goal in this match. A mistake from Klavan let in Rodriguez and after the forward found teammate Redmond inside the penalty area, he made no mistake in converting the ball into the bottom corner.
24 minThat goal has rocked Liverpool to a certain extent. They had controlled the opening 17 minutes without creating much and they have been made to pay by a Southampton team who are growing in confidence in this game.
27 minKlopp doesn't look very amused on the touchline. While his team are dominating possession, they aren't creating much which will cause any alarm to Forster. There's not a lack of urgency in the final third but they are a bit lethargic in midfield.
31 minWe are a third of the way through this match and we remain at 1-0. We've not seen much of Southampton in the final third but they lead thanks to that clinical finish from Redmond. Puel will be pleased with how this is going.
35 minThere are three former Southampton players in the Liverpool side tonight - Clyne, Lovren and Lallana - but they have all made little impact. Lovren is getting booed every time he touches the ball after the way he left St Mary's for Anfield.
37 minBit better from Southampton as Rodriguez miscues a shot wide of the target but in all fairness to the Saints player, it got a slight deflection. From the resulting corner, Clasie got a volley on goal from about 30 yards but it was straight at Karius.
40 minKlopp is becoming increasingly irritated on the touchline. I don't think he will be holding back at half time. Liverpool are still playing at a pedestrian pace and it is suiting Southampton.
43 minCHANCE! How important will this save be? Tadic does superbly to find Redmond at the back post and the attacker should score from eight yards. However, his first-time effort is too close to Karius who pulls off a terrific save.
8.32pmThe half-time whistle goes at St Mary's and Southampton head into the break with a deserved 1-0 advantage thanks to that cool finish from Redmond. Liverpool haven't been at the races and it probably won't be long before we see Coutinho and Origi.
46 minWe are back underway. It doesn't appear that he have had any changes. That will probably change should Liverpool not improve during the opening 15 minutes.
48 minIt's been a strong start to the second half from Southampton and Cedric does well to win a free kick out of Milner on the edge of the area. Tadic gets a shot in on goal but Milner diverts the ball away for a corner. Not sure Tadic should have been shooting from there.
52 minI really can't understate how poor Liverpool have been so far. They offered very little in the first half and since the restart, they've only had one burst forward. Southampton look like they want this a lot more than the visitors.
55 minThe home side are certainly getting ambitious now. Van Dijk has just gone on a surging run down the left and he somehow managed to get to the byline. Unfortunately for the Saints, he didn't look up and instead focused on blasting the ball across goal, with the ball being claimed by Karius.
58 minSturridge is cutting a very frustrated figure right now. He's having one of his worst games in a Liverpool shirt and it will come as no surprise if he is replaced by Origi sooner rather than later.
59 minSHOT! Lallana is provided with the chance to get a shot in on the edge of the box but he hits his effort on the turn and it goes harmlessly wide. He rushed that - another sign of frustration in the Liverpool ranks.
60 minSHOT! Liverpool have been better over the last couple of minutes but they still aren't testing Forster as Firmino shoots straight at the goalkeeper. Time for a change...
62 minSUBSTITUTION! Klopp decides enough is enough and introduces Coutinho, who replaces Wijnaldum.
65 minBOOKING! Tadic is being fouled by Clyne but the referee gives nothing, much to the annoyance of the Southampton midfielder. His complaints earn him a yellow card.
66 minCHANCE! Huge chance for Southampton! A blistering break involving Redmond sees the attacker play in Cedric who is clear on the right-hand side of the penalty area. Rodriguez and a Liverpool defender are in the middle but he decides to shoot towards the near post from 12 yards and gets it all wrong.
70 minJust 20 minutes to go at St Mary's. It's becoming a lot more end to end but clear-cut chances remain few and far between. There's no doubting that Southampton would take this scoreline but they are throwing men forward to score a second.
73 minSUBSTITUTION! Clasie has picked up a knock for Southampton so Pierre-Emile Hojbjerg is coming on in his place.
78 minI'm really surprised that Klopp hasn't decided to replace Sturridge with Origi. The England international hasn't contributed anything positive tonight and Origi has already shown this season that he can make an impact off the bench. Southampton continue to look comfortable.
82 minBOOKING! Rodriguez picks up a yellow card for a foul but it's his last contribution as he is replaced by Shane Long. James Ward-Prowse has also come on in place of Davis.
83 minSUBSTITUTION! Divock Origi finally sees some action as he replaces Firmino.
83 minWOODWORK! Redmond comes within inches of netting his second goal of the night! After Long got free down the left, he found Redmond at the back post but his dinked effort over Karius hit the underside of the crossbar before being cleared by a defender. So unlucky and at the same time, a huge let-off for Liverpool.
88 minSouthampton seem in two minds about whether to go for a second or try to see out a 1-0 win. Liverpool are trying to capitalise but the home side remain resolute at the back.
90 minThere will be four minutes of added-on time.
90+2 minSHOT! Coutinho hasn't been very effective since his introduction and another 30-yard strike goes harmlessly into the stands. There's definitely signs of rust on the Brazilian's boots.
9.40pmThe full-time whistle goes at St Mary's and Southampton have held on to complete a deserved 1-0 win thanks to an early goal from Nathan Redmond. The Saints will think that they should have won by a wider margin, though, after wasting a number of chances against a below-par Liverpool side. There's still all to play for in the second leg in two weeks' time.
9.40pmThat will be all from Sports Mole for this game. Thank you for joining us this evening and we hope to see you again real soon. Goodbye for now.