Luciano Becchio's first-half strike briefly threatened an upset for the hosts but goals after the break from Juan Mata, Branislav Ivanovic, Victor Moses, Eden Hazard and Fernando Torres wrapped up a convincing win for the Blues.
Victory gives Rafa Benitez's chances of bringing silverware back to Stamford Bridge a timely boost, having already presided over exits from the Champions League and Club World Cup.
Much was expected of the first meeting between these two historic rivals in over eight years but events on the pitch only served to show the gulf which has emerged between them.
Benitez shuffled his pack after Sunday’s 1-0 defeat to Corinthians, handing Marko Marin and Ryan Bertrand rare starts and recalling Oscar. Neil Warnock, meanwhile, made three changes to the side which defeated Ipswich Town 2-0 on Saturday, with Jamie Ashdown, Jason Pearce and Michael Brown replacing Paddy Kenny, Alan Tate and David Norris.
Leeds attacked with conviction from the start but it was Chelsea who conjured the first chance on six minutes – Oscar playing in Moses, whose fierce low drive was beaten away by Ashdown.
The visitors appeared to be taking control and Moses stung the palms of Ashdown again before Mata's goalbound effort was deflected behind by Pearce.
Benitez's men were dominating possession but a mistake from David Luiz saw them go behind on 37 minutes. The advancing Brazilian's dinked pass was intercepted by Sam Byram and the flowing counterattack which followed ended with Becchio sweeping home his 16th goal of the season.
Chelsea came roaring back and Moses had the ball in the net on 42 minutes after a flowing move, only for the assistant referee to rule that Torres had strayed offside in the build-up.
Ashdown twice parried away dipping Lampard drives from distance and Leeds went into the break with their noses in front.
Chelsea levelled the scores a minute after the restart, however, asMata capped a neat passing interchange with a low curling effort which crept under the palm of Ashdown and trickled in.
On 64 minutes Chelsea went ahead as Ivanovic powered home a header at the near post from an inviting Lampard delivery.
Chelsea were playing with swagger now and almost immediatelyMoses cut inside from the left and rifled a shot past Ashdown.
With the game already over as a contest, Luiz played a raking pass through for substitute Hazard, who calmly slotted home a fourth.
The Leeds defence were now virtually non-existent and, after Ashdown parried another Lampard shot, Hazard squared the ball for Torres to tap into an empty net.
Having suitably humbled their hosts, Chelsea then eased to victory, joining Swansea City, Aston Villa and Bradford City in the semi-finals.