A committed defensive performance, punctuated by the Ivorian's breakaway goal just before halftime, secured the hosts a slim advantage ahead of the Camp Nou return leg.
Alexis Sanchez hit the bar early on and Cesc Fabregas had a weak effort cleared off the line before Drogba finished a smart break in first-half stoppage time.
The Blues then shut Barca down effectively in a chance-scarce second period, until Pedro hit the post and Sergio Busquets launched the rebound feebly over at the death.
The stunning opener against Tottenham on Sunday convinced Roberto Di Matteo to pick Drogba up front at Fernando Torres’ expense, with Gary Cahill replacing the injured David Luiz. Raul Meireles and Branislav Ivanovic were also both recalled.
Pep Guardiola opted for Javier Mascherano ahead of Gerard Pique at center back, with Fabregas starting against a Blues side he knows well and Lionel Messi seeking to end a record of six games without scoring against Chelsea.
Barca immediately began dominating possession but Drogba posed problems early on, a canny flick to burst free of Mascherano let down when the remaining defender, Puyol, intercepted his looser second touch.
The visitors’ patient build-up was suddenly punctuated, though, by an Andres Iniesta through-ball that bypassed Chelsea’s defense and found Sanchez free in the area. He deftly dinked it over Petr Cech but unluckily saw it come back off the crossbar.
A hairy moment in the opposite box followed when Chelsea’s long throw almost broke for John Terry, but Dani Alves just scraped it away in time.
Barca was not yet producing its best but should have been in front after 16 minutes. Messi dragged two defenders out of the way before cutting back to Iniesta, whose shot was parried by Cech. The rebound came to Fabregas but he inexplicably miskicked wide.
Midway through the half Barca was slowly turning up the pressure. First Fabregas forced a near-post save from Cech before Messi leapt on the edge of the box to head a Sanchez cross into the stretching keeper’s arms.
A patchy period followed with a few niggling fouls and no great creation. Chelsea was quashing much of the Catalonians’ attacking prospects.
The English club's resistance was nearly broken on 42 minutes, however, when Barca broke with Messi. The Argentine slid in Fabregas to his left, but his colleague’s attempt to lift it gently over Cech was too underpowered and Ashley Cole arrived to clear off the line.
Halftime parity seemed inevitable but, in added time, Chelsea suddenly broke. Ramires controlled well on the left flank and slipped a perfectly weighted pass across the box, where Drogba was waiting to finish just past the grasping Victor Valdes.
Barcelona probed after the break, Adriano cutting in on his right foot to send Cech flying to his left to save, but Chelsea’s first corner moments later saw Lampard’s swinger narrowly evade two blue shirts on its way past.
Sanchez came close again when Fabregas’ inventive scoop over played the Chilean in at point-blank range, but he had little space to aim into and poked the ball wide.
The half dragged on with little extra purchase for the visitors. Messi attempted more than one run forward from deep into the box but was thwarted first by Cahill and then Terry, with Pedro introduced by Guardiola in place of Sanchez in the hopes of better testing the resilient Blues.
It had little effect, though, with clear-cut chances absent and the visitors, short of ideas, looking unlikely to force their way through. As they pushed up in desperation, Drogba was able to battle past on the break, but his through-ball into the path of substitute Salomon Kalou on 80 minutes was a touch too strong and the opportunity winked out.
Kalou nearly stole a second as he slipped around the outside of the last defender to receive a high ball but, with Valdes bearing down, he lifted his effort well over.
One of Barca's closest moment in the second half came when Messi's 87th-minute free kick was flicked on by a crouching Puyol. Substitute Thiago Alcantara flashed at it but couldn't make contact, yet Cech still had to do well to dive and parry.
The visitors, though, should really have equalized at the very last. Despite Terry's initial excellent tackle to snuff out one chance, Pedro sliced a shot against the post before Busquets, with the goal at his mercy, lofted the ball disastrously over to ensure that the Blaugrana will return to Camp Nou behind on aggregate.
Follow GOAL.COM on