The Ivorian striker drilled home a low finish on the stroke of half-time after an uncharacteristic error from Lionel Messi allowed Chelsea to counter attack.
Barcelona had dominated the match, barely giving up possession and missing a host of gilt-edged chances, including glaring misses from Cesc Fabregas and Alexis Sanchez.
Sanchez also hit the bar in the first half, while Pedro saw a last-gasp drive rattle off the post with Sergio Busquets blasting the rebound over.
Petr Cech played his part too, making smart saves from Adriano and - late on - Carles Puyol, as Chelsea stuck to a gameplan with some effect, although they rode their luck and then some.
The victory goes some way to helping banish the memories of Chelsea’s controversial semi-final exit to the Catalans in 2009, this edition's referee Felix Brych far more capable in his handling of gamesmanship from both sides than poor Tom Henning Ovrebo, whose reputation took a pounding after failing to award the West London side any of four penalty appeals in that match.
But, for all the home side's celebrations afterwards, the job is barely half done with Barca clear favourites for the second leg next week, and Messi expected to show his true colours at the Camp Nou.
The stock of both sides has changed somewhat since that night three years ago, with Barca widely-regarded as the best side in the world while Chelsea have fallen from grace, although a resurgence under Roberti Di Matteo bodes well for the future.
As a result, Barca were always going to take the game to a Blues side who - in the parlance of their manager back in ’09 - parked a double-decker Routemaster bus around Messi, who was effectively marked out of the game.
It would have been lunacy for Chelsea to do anything else, and they set up accordingly, with Drogba the lone striker spearheading a five-man midfield boasting four centrally-minded players.
Barca still hogged the ball and even the most partisan Blue would admit that Chelsea were fortunate not to be three goals down by half-time, let alone one to the good.
The first major opportunity fell to Sanchez, who hit the bar on nine minutes after he was played onside by Ashley Cole.
Fabregas then missed a sitter, scuffing his finish wide after Cech failed to hold on to Andres Iniesta’s low drive.
Iniesta had a penalty appeal waved away when Gary Cahill dispossessed him in the area, the England defender’s boot definitely taking the ball but his use of the arm to ease away the Spain star was a touch dubious.
For all their backs-to-the-wall defending, Chelsea were firing warning shots on the break: Drogba was let down by his touch on a couple of occasions after fine strength and movement to pull away from a back two of Puyol and Javier Mascherano, who struggled at times.
Again Fabregas missed an opportunity to give the Catalans a lead, sent through by Messi and clipping a deft finish over Cech but denied on the line by Cole.
Drogba, meanwhile, was putting himself about, a blast from the past in every way as he looked to bully Barcelona’s defence in the air, while delaying play with his usual grass-based theatrics.
And, deep into injury time at the end of the first half, the Ivorian big-game specialist made his mark, thanks in part to an error from Messi.
The Argentine gave the ball away, allowing Frank Lampard to scoop a high pass to Ramires bounding down the left: the Brazilian had a sight of goal but, at a tight angle, kept his cool to drill a low ball across the sliding Mascherano and Puyol for Drogba to gobble up a low finish at the far post.
The second half had a similar pattern to it: Barca stroked the ball around patiently to create openings, Chelsea looking for counters and set plays.
As with the first 45, Barca spurned several chances. Sanchez was denied by a fine Cahill tackle and later put wide under pressure from Cole after being sent clean through by a scooped pass from Fabregas and then Adriano had a curling drive well saved by Cech.
Messi, meanwhile, was toiling as Chelsea happily sat back for a good half hour, Barca generating pretty patterns but kept at bay by some determined defending.
The final minutes saw the inevitable rally as Barca threw everything at Chelsea, with Cech alert and agile to keep out a Puyol header from a clever Messi free-kick, the trick-option the only way Pep Guardiola's diminutive stars would beat the bigger team in the air.
And, with Chelsea holding Barca off by fair means and foul, the final minute of injury time saw Barca miss a golden opportunity to get an away goal. Messi’s low ball in was delightfully backheeled by Busquets, with Terry’s intervention staving off one finish but allowing Pedro to drill a low shot past Cech. It hit the post and, with the goal at his mercy, Busquets could only hammer the ball clear of the crossbar.
It was the kind of late drama to befit a Chelsea-Barca tie, and one that bodes well for the neutral next week. Fans of both clubs, though, can expect a nail-biter at the Camp Nou.