A shock was on when Leeds went in at halftime 1-0 up thanks to Luciano Becchio's 37th-minute goal at a rain-soaked Elland Road.
However, Chelsea was clinical after the break, equalizing through Spain playmaker Juan Mata in the 47th before adding four more goals in a ruthless 19-minute spell. Branislav Ivanovic, Victor Moses, Eden Hazard and Fernando Torres were the scorers for the European champions, who have won the League Cup four times — most recently in 2007.
"We had a word with ourselves at half time and the early goal gave us an impetus to go on and win it," Chelsea captain Frank Lampard said.
By moving into the last four, where it is also joined by Aston Villa and fourth-tier Bradford, Chelsea went some way to making up for the frustration of losing the Club World Cup final to Corinthians 1-0 on Sunday. A disappointing December began with elimination from the Champions League, ending a title defence that lasted barely six months.
With the rain pouring down and a slightly under-strength Chelsea only back from a draining trip to Japan on Monday, conditions had been ripe for an upset in what has been a season of surprises in the competition.
"The reaction in the second half was fantastic, especially with travelling back from Japan and having jet lag," Chelsea interim coach Rafa Benitez said. "We were looking for character and the reaction was so good."
Leeds would have loved nothing more than to get one over a team that has been one of its big rivals since the mid-1960s and '70s, when they were arguably the two leading clubs in England.
Police were on high alert for trouble but the match appeared to pass off without major incident off the pitch, although there were some strong tackles on it in the early stages. Lampard was booked for one particularly tough challenge on former Senegal forward El-Hadji Diouf, one of the most volatile players in English football.
An upset was on the cards when Becchio slotted home a low cross by Jerome Thomas eight minutes before the break, the most incisive moment of a hard-fought first half.
Yet, Chelsea soon displayed a ruthless side that was sorely lacking against Corinthians, having 10 shots on target in the second half and scoring from five of them.
Mata jolted Leeds by squeezing in a shot from the edge of the area, with goalkeeper Jamie Ashdown perhaps at fault.
Then the floodgates opened, with substitute Eden Hazard helping Chelsea run amok.
Ivanovic headed in Lampard's left-wing corner to the near post in the 64th and Victor Moses drilled in a shot from 20 yards two minutes later.
Eden Hazard run onto a fine through-ball from marauding centre back David Luiz for the fourth in the 81st and Torres finished off Leeds, tapping in from Hazard's cross.
"They took over and we could not cope," Leeds manager Neil Warnock said.