The Ivory Coast striker struck a superb shot from the edge of the penalty to settle a meeting of the two teams expected to qualify from Group A.
But although the result leaves Chelsea sitting pretty on nine points from three games, Barcelona will need to improve on their comparatively paltry return of four if they are to retain their European crown won so convincingly last season.
The Spanish champions accounted for Chelsea in the Champions League last season, but with Michael Ballack, Andriy Shevchenko and Ashley Cole added to the ranks in the summer, the Blues look an altogether more solid and cohesive unit in Europe.
Barcelona were first to threaten and stand-in goalkeeper Henrique Hilario silenced any doubts over his selection with a fine low save from Leo Messi after 24 minutes.
With regular keepers Petr Cech and Carlo Cudicini sidelined with head injuries, the Portuguese custodian responded with an assured performance and followed up his opening save with an even better one at the base of his near post from Xavi soon after.
Ronaldinho and Messi combined in extravagant fashion to create the opening, but Hilario got down well to smother the ball.
In between, Rafael Marquez prevented Shevchenko from forcing the ball over the line after Drogba's shot under the body of the keeper had been blocked.
With the second half barely seconds old, Drogba struck in decisive fashion, but even after the opening goal it was Chelsea who always looked the more likely to score again.
Shevchenko should have doubled the advantage after 55 minutes when Frank Lampard's square pass found him unmarked just inside the penalty area, but the Ukraine striker hurriedly lashed high over the bar.
Victor Valdes then kept Barcelona in the game as he denied Michael Essien the chance to stab the ball home from close range following Drogba's initial effort.
Barcelona coach Frank Rijkaard made three quick-fire changes in the second half, but it failed to pep up his strangely out-of-sorts attacking force of Ronaldinho, Messi, Deco and Chelsea old-boy Eidur Gudjohnsen.
And even when the visitors did manage to find a way through, they simply ran into a defensive wall that wasn't going to budge an inch on the night.