The Ivory Coast striker scored early and provided the impetuous for a comfortable victory, with further goals from Michael Ballack, Daniel Sturridge and Salomon Kalou.
Cardiff had a glimmer of hope when Michael Chopra equalised but it was never really enough to trouble Chelsea.
The visitors suffered the worst possible start when, after just two minutes, a floated pass by John Obi Mikel saw Drogba beat the Cardiff offside trap.
He raced into the Welsh club's penalty area and calmly slotted home past a helpless David Marshall.
The Bluebirds responded well to the setback and on six minutes Alex was forced to clear off the line from a Gabor Gyepes six yards out.
Four minutes later and Henrique Hilario produced a fine save from Anthony Gerrard and, from the resultant corner, Chopra somehow hooked the ball over the Chelsea crossbar.
Drogba produced a nice piece of skill - performing an overhead kick on 26 minutes - but the shot was not powerful enough to trouble Marshall.
On 34 minutes, Cardiff equalised deservedly through Chopra. The striker took advantage of lax marking and met Chris Burke's left-wing cross perfectly to direct a downward header past a flat-footed Hilario.
A flashing 20-yard drive by Sturridge two minutes from the break was inches wide of restoring the Blues' lead, while Joe Cole was replaced at half-time by Kalou.
Drogba had the first effort of the second half - a 25-yard free kick which curled at the last moment but not enough to fool impressive Marshall.
On their second attack on 52 minutes, the home side scored. Deftly sidestepping the Cardiff centre-back's, Ballack latched into a perfect though ball from Drogba and the German captain flicked the ball over Marshall with the outside of his left foot and in to the net.
Number three came out of the blue on 69 minutes. Sturridge was fortunate with his one-two with Drogba on the edge of the Cardiff area and the ball fell kindly to the young English striker 12 yards out and he stroked home a low left-footer into the net.
Cardiff countered on 81 minutes and right-back Kevin McNaughton was unlucky to see a sizzling left footer inch wide of Hilario's left upright.
Number four came five minutes from time. Substitute Florent Malouda fed the ball wide on the right to Paulo Ferreira and the Portugal defender arced across a fine right footed ball which Kalou redirected powerfully with a firm header from 10 yards out.