The Blues started brightly with the lively Ashley Cole a constant thorn in the away team's side, shooting wide of the target after an incisive passing move from Drogba and Nicolas Anelka.
Stoke, though, were determined not to sit back and absorb constant pressure from the home side and Dean Whitehead characterised their never-say-die spirit with a right-footed strike that forced a decent save from Petr Cech.
With less than ten minutes of the match played, however, it looked like Chelsea were going to be set on their way to another excessive scoreline when Malouda went down in the box under a challenge from Ryan Shawcross to win a spot-kick.
Frank Lampard's penalty kick was, however, a tame effort and Thomas Sorensen kept Stoke in the game with a good save.
Michael Essien and Drogba both wasted clear-cut chances to rectify Lampard's saved effort shortly after but it was left to Malouda to apply a finishing touch of any real note just after the half-hour mark, with the Chelsea man sending a neat finish past Sorensen after a pinpoint pass from John Terry.
Cole almost added a second goal shortly after but saw his shot from inside the box crash off the bar as Stoke defended resolutely until the break to keep their hopes of getting something from the game intact.
For large parts of the second half, Stoke looked more than worthy of grabbing an equaliser and the home side were fortunate to have Drogba on hand to clear an effort from Matthew Etherington off the line just moments after the Chelsea striker made a mess of a close range header at the other end.
Glenn Whelan almost scored the goal that Stoke's play merited with a thunderbolt of a shot that smashed against the crossbar but Chelsea wrapped up the three points with a second goal less than 15 minutes from time.
This time it was Anelka who won a penalty for the home side after going down under a challenge from Sorensen and Drogba made no mistake in smashing the ball past the helpless Stoke goalkeeper.