Luciano Becchio had given the Championship outfit the lead against the run of play in the 37th minute in the teeming rain in West Yorkshire, only for the Blues to show their superiority after the interval, although the final scoreline was harsh on the home side.
Jamie Ashdown, who made several good stops, was culpable right at the start of the second period as he allowed Juan Mata's low long-range effort to slip under his hand before Branislav Ivanovic and Victor Moses grabbed two in three minutes shortly after the hour mark.
With Leeds pushing for a way back into the contest and with their legs clearly beginning to tire, substitute Eden Hazard put the finishing touch to David Luiz's excellent through-ball in the 81st minute before setting up Fernando Torres to tap home the fifth.
The Blues were quickly out of the blocks and Moses forced a good save from Ashdown after being found by Oscar on the slick Elland Road surface. Captain Frank Lampard went into the book in the 15th minute after going through the back of El-Hadji Diouf, following an earlier foul on Sam Byram.
Chelsea appealed in vain for a penalty in the 23rd minute when Moses tumbled in the box after brief contact with Michael Brown, with referee Andre Marriner not interested and the Blues man picking himself up to test Ashdown again.
Mata put Brown on his backside on the edge of the box only to see his shot diverted behind for a corner, before Leeds took the lead against the run of play after hitting Rafael Benitez's side with a lightning counter-attack in the 37th minute.
Centre-back Luiz advanced deep into Leeds territory, only to see his pass cut out by Tom Lees' head and picked up by Michael Tonge. The midfielder's searching pass out to Jerome Thomas on the left flank was followed by an outstanding ball across the box which Becchio rolled beyond Petr Cech and into the bottom corner with aplomb.
That sparked an immediate response from the Blues prior to the interval with Moses seeing a goal ruled out for offside and Ashdown called into action to superbly deny Lampard's dipping long-range free-kick, while Lees headed narrowly over from a Diouf cross at the other end.
Neil Warnock would surely have warned his side to be on their toes at the start of the second period, but it took less than two minutes for Chelsea to level, with Ashdown allowing Mata's low first-time shot from outside the box to squirm under his hand and into the net.
The introduction of Hazard from the bench in the 60th minute inspired Chelsea, with Ivanovic heading home a corner at the near post to put the Blues in front before Moses drilled home from 25 yards, with Ashdown beaten at his near post, although there was precision and power in the shot.
Brazil international Luiz then opened up the home defence with a searching pass to Hazard which the Belgian ran onto before finishing with aplomb, before Ashdown was beaten for a fifth time after beating out Lampard's shot, only to see Hazard pick up possession and feed Torres for a chance which simply could not be missed.