Liverpool laid siege to Southampton's goal in the second half having been outplayed in the opening 45 minutes, but the visitors were doggedly determined to keep the hosts at bay and poached a winner at the death to seal a 2-0 aggregate victory.
Southampton had chances to put the tie to bed in the first half, with Dusan Tadic and Steven Davis guilty of poor finishing, but after the break it was all Liverpool and Daniel Sturridge wasted two superb chances.
With the seconds ticking away, Liverpool felt they should have had a penalty when Divock Origi appeared to be tripped in the area, but Southampton broke swiftly and substitute Long blasted a shot past Loris Karius.
Southampton, who have sold millions of pounds worth of players to Liverpool in recent seasons, will face either Manchester United or Hull City in the final.
United will take a 2-0 lead into the semi-final second leg at Hull on Thursday.
Southampton's victory continued a remarkable run that has seen them shut out Crystal Palace, Sunderland, Arsenal and now Liverpool, the Premier League's top scorers.
The Saints, who have not won a major trophy since lifting the FA Cup in 1976, arrived at Anfield with a gameplan that worked to perfection as the visitors sat back and let Liverpool have the ball, while looking to spring fast, incisive counter attacks at every opportunity.
Nathan Redmond, who scored the only goal of the first leg when he also missed a bagful of chances, was a persistent nuisance for Liverpool's defenders, who were frequently exposed by the winger's pace and trickery.
Redmond's slalom runs from deep created the first half's best two chances as he first teed up Tadic, who could not beat Karius from close range, and then laid on a superb opportunity for Davis, who blasted over from 10 metres.
Having been thoroughly outplayed in the first half, Liverpool stirred into life after the break.
Their first sniff of goal came when Emre Can's effort from distance slipped through the grasp of Fraser Forster who then had to make a drastic last ditch save to claw the ball off the goalline.
The hosts' best opportunities, however, fell to Sturridge who first ballooned an acrobatic volley over the bar from five metres and then sidefooted a cross off target with just the keeper to beat.
With the game entering injury time, Origi went down under a challenge from Jack Stephens, but referee Martin Atkinson waved the penalty appeals away and Southampton broke at pace.
Josh Sims ran 60 metres before feeding Long, who took a touch and thrashed the ball past Karius.
(Reporting by Toby Davis; editing by Ed Osmond and Pritha Sarkar)
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