Leeds, currently mid-table in the Championship, sensed a quarter-final shock when they took a 38th-minute lead thanks to a 15th goal of the season from Argentinian striker Luciano Becchio, who slid the ball home from 12 yards as he met a Jerome Thomas cross to round-off a length of the field move.
But defender Tom Lees missed a great chance to double the advantage in first-half stoppage-time, heading over from an El Hadji-Diouf cross as the Yorkshire club attempted to emulate their neighbours Bradford City, who booked their semi-final place with a stunning upset over Arsenal.
Chelsea refused to go the same way as their Premier League rivals, moving through the gears to score five second-half goals to make it through to the last four in January in some style.
They were level 60 seconds after the re-start when Leeds goalkeeper Jamie Ashdown allowed Juan Mata's weak 20-yard shot under his grasp on the greasy surface, the ball finding the bottom corner.
Two goals in as many minutes midway through the half sealed victory in Chelsea's eighth game in 24 days, a little over 48 hours after their return from defeat against the Brazilians Corinthians in the Club World Cup final in Japan.
Branislav Ivanovic stole in at the near post to head home a corner on 64 minutes to give the visitors a lead they wouldn't relinquish as they moved a step closer to claiming their first silverware under Benitez, the interim manager.
The win will give the Spaniard further ammunition in his battle to win over a large section of Chelsea support who have been vocal in their protest at the sacking of Roberto Di Matteo, and the choice of the former Liverpool manager as his replacement.
Man-of-the-match Victor Moses made it three after 66 minutes, rounding-off a neat three man move with Fernando Torres and Mata to fire past Ashdown from 20 yards.
Chelsea waited until the final 10 minutes to assert their authority with two further goals as Leeds tired and left gaps in a failed attempt to find a way back into the contest.
Substitute Eden Hazard made it four with a calm finish beyond a stranded Ashdown inside the box after latching onto a superb 40-yard through-ball from David Luiz, who made amends for his mistake that led to Leeds breaking the deadlock.
Hazard was involved in the fifth with seven minutes remaining, squaring for Torres to tap home his 13th goal of the season after pouncing on the loose ball after another fine save from the over-worked Ashdown.