The hosts had looked set to cause another upset when Luciano Becchio shot them ahead in the 37th minute, to give Leeds an unlikely 1-0 lead at the half.
But a superlative display by the European Champions in the second half saw them turn the match around.
First, Victor Moses teed up Juan Mata just two minutes after the restart, and the Spanish gladly took the chance, and grabbed the equaliser.
Then the Nigerian took matters into his own hands in the 66th minute, when he meandered through Leeds defence, to slam an unstoppable shot past Jamie Ashdown in goal for Leeds. But that was two minutes after Branislav Ivanovic headed in a Frank Lampard corner for Chelsea's second.
Eden Hazard came on for Marko Marin to score the fourth on 81 minutes, and Fernando Torres added gloss to the scoreline with a fifth, after unselfish play by Eden Hazard.