Jurgen Klopp’s side clinched their first domestic knockout prize since the 2012 League Cup when Kepa blazed his spot-kick high over the bar.
It was the only miss in the nerve-jangling shoot-out, which saw Liverpool keeper Caoimhin Kelleher score his penalty just before Kepa failed.
Ironically, Kepa was sent on at the end of extra-time to replace Edouard Mendy given his reputation as a penalty saving specialist, but the Spaniard was unable to repel any of Liverpool’s kicks.
While there were no goals in 120 minutes, this was a fascinating final which produced countless chances for both sides to win it before the cruel denouement.
Liverpool saw Joel Matip’s second-half goal controversially disallowed for a marginal offside against Virgil van Dijk, while Chelsea had three goals ruled out for offside later in the match.
The Reds have lifted the League Cup a record nine times, moving ahead of Manchester City, while Klopp is the first German manager to win the tournament after finally tasting Wembley success following two previous defeats as a boss there.
Liverpool remain in contention for an unprecedented quadruple after closing the gap on Premier League leaders Manchester City to six points with a game in hand.
They are on course for the Champions League quarter-finals after a last 16 first-leg win at Inter Milan and host Norwich in the FA Cup fifth round on Wednesday.
While the match was a memorable occasion, there was a sombre beginning as Liverpool and Chelsea players united in a show of support for war-torn Ukraine.
Amid the Russian invasion of its neighbour, Chelsea skipper Cesar Azpilicueta and Liverpool captain Jordan Henderson carried flowers in the country’s yellow and blue colours onto the pitch.
Both teams stood for a minute’s applause, while a message on the stadium scoreboard in yellow and blue read “Football Stands Together“.
For Chelsea, this was a painful end to a difficult week, which saw Chelsea’s Russian owner Roman Abramovich on Saturday announce that he is “giving trustees of Chelsea’s charitable foundation the stewardship and care” of the club.
Abramovich, who will remain the club’s owner, made the move after calls in the UK Parliament for Russian oligarchs to be stripped of their assets.
Now Chelsea must focus on retaining the Champions League, while aiming for a top-four finish and a potential return to Wembley in the FA Cup.