Southampton will go into their EFL Cup semi-final second leg at Liverpool with a 1-0 lead, but could have headed to Anfield with more after a dominant display at St Mary's.
Saints took the lead on 20 minutes through Nathan Redmond, finishing past Loris Karius after Jay Rodriguez pounced on an error from Ragnar Klavan.
Southampton had the better of the chances in the second half too, with Cedric Soares missing the chance to test Loris Karius having been put through on goal by Redmond, before Redmond himself saw a lofted effort came off the crossbar late on.
The second leg will be played at Anfield on January 25, and the winner will play either Hull or Manchester United in the final at Wembley, with United holding a 2-0 lead going into the second leg following their win on Tuesday night at Old Trafford.
Jurgen Klopp made eight changes from the side that was held 0-0 by Plymouth in the FA Cup on Sunday, while Saints made seven changes of their own.
Roberto Firmino forced a fine save from Fraser Forster after lashing an effort on target from Adam Lallana's ball over the top of the defence, before Karius kept out Redmond's far-post effort as the ball dropped to him kindly.
Saints were ahead shortly after as Klavan's scuffed clearance fell to Rodriguez, who played in Redmond to finish past Karius with a low effort from 15 yards out.
Karius came to the rescue again for Liverpool just before the break, pulling off a fine stop to deny Redmond again after Dusan Tadic's cut-back had found him in acres of space at the far post.
Philippe Coutinho was on the bench for the first time since suffering ankle ligament damage in November, and was introduced with half an hour remaining, but it was Saints again who had the better of the chances as the second half wore on.
After a fine break by Redmond on the right wing, Cedric was played in on goal, but instead of going across the goalkeeper could only find the side-netting at the near post.
Redmond had another fine chance to take a healthy lead to Anfield in the 83rd minute after being played through on goal by a square Shane Long pass, but having lifted the ball over Karius, the ball hit the crossbar, bounced off Dejan Lovren and was cleared
Liverpool pressed late on, but could not find a leveller, while the Saints will be wondering how they are only heading to Anfield with a one-goal advantage given their dominance on Wednesday evening.