Southampton ended a 38-year wait for a League Cup final appearance as Shane Long's late strike sealed a 1-0 semi-final second-leg victory at Liverpool, winning the tie 2-0 on aggregate.
The Republic of Ireland international struck deep into stoppage-time at Anfield, seconds after Divock Origi had a penalty appeal declined, as last season's runners-up were denied a return to the Wembley showpiece.
Just as they had in the first leg, Southampton spurned a host of chances to put the tie to bed, but it proved immaterial as their defence - missing the injured Virgil van Dijk - became the first side in League Cup history to reach the final without conceding a goal.
The victory sees Claude Puel seal Saints' first major final appearance since the 2003 FA Cup, with either Hull or Manchester United - who play live on Sky Sports on Thursday - lying in wait on February 26.
After their shock Premier League defeat to Swansea on Saturday, Klopp welcomed back Joel Matip, who made his first start since December 11 after his lengthy eligibility dispute with the Cameroon national team and FIFA was resolved.
The centre-back was one of three changes made by Klopp, who recalled Loris Karius, Trent Alexander-Arnold and Daniel Sturridge into the starting line-up.
With Southampton missing Van Dijk due to injury, Jack Stephens deputised in the heart of the Saints defence, while Steven Davis, replacing Pierre-Emile Hojbjerg, took the armband.
Southampton could have been out of sight ahead of the trip to Anfield had they converted their chances in a dominant first-leg at St Mary's and, after an even start, their wastefulness resurfaced with the visitors spurning the best chances in the first period.
First, Nathan Redmond's cut-back on 36 minutes presented Dusan Tadic - six yards out - with a clear sight of goal, only for a sprawling Karius to thwart his effort.
Redmond continued to cause havoc, racing away from Alexander-Arnold three minutes later before his cross fell perfectly for Davis, who lashed wildly over the target.
With just 45 minutes standing between Southampton and a place in the final, nerves threatened to derail their hopes as goalkeeper Fraser Forster parried Emre Can's fierce drive towards his own goal on 54 minutes.
Thankfully for the Saints, though, the England international produced an excellent recovery to claw the ball from off the goal-line, with the Goal Decision System ruling the ball had not crossed the line.
That lifted the spirits of the Anfield faithful, but Liverpool could not convert that into goals as they were proving wasteful in front of goal themselves.
Sturridge sliced a glorious chance over from six-yards out on the hour, before the England striker turned Jordan Henderson's cross over the bar four minutes later.
As frustration set in for the hosts, the Saints backline grew in confidence, Philippe Coutinho's wide effort on 78 minutes the closest they came to levelling to tie.
In desperation, Liverpool appealed for two penalties, the first an alleged Long handball on 84 minutes before Stephens' challenge on Origi went unpunished in the 90th minute - both of which referee Martin Atkinson ignored.
Stephens' challenge resulted in a Liverpool corner but, instead of yielding an equaliser, Southampton killed the tie off, breaking with pace on the counter as substitute Long rifled the ball past Karius to seal a famous victory.