Drogba scored with a low shot from just inside the area in the 47th minute as Chelsea largely outplayed the defending champions at Stamford Bridge.
Chelsea has a maximum nine points from three games, while Barcelona was tied with Werder Bremen on four points.
"I think the team played very, very well," said Chelsea manager Jose Mourinho. "Every individual played well and we played well as a team. I think that we deserved the three points.
"But it's not a moment to be crazy. We got three points. I don't think it's a reason to be jumping about."
Although Chelsea had the better chances and possession, it needed goalkeeper Hilario - who was playing only because Petr Cech and backup Carlo Cudicini both had head injuries - to save shots from Lionel Messi and Xavi Hernandez in the first half.
The Portuguese goalkeeper also safely held a 30-meter (yard) free kick from Ronaldinho under the crossbar.
"Hilario showed security from the first minute," Mourinho said. "The team gave him confidence and he gave confidence to the team."
Chelsea took control in the second half and went ahead. Left back Ashley Cole put the ball in from the left and Drogba turned past Carles Puyol before scoring his fourth Champions League goal of the season.
"It was a tight, close game until Drogba changed all that," said Barcelona coach Frank Rijkaard, who took off a defender after the goal to try and put pressure on the home side.
"I think I was right to take some risks by going three at the back and try and get something out of the game.
"But Chelsea are a great side and tough when they go ahead."
Rijkaard said he remained confident Barcelona would make it to the last 16.
"What we have to concentrate on at the moment is not whether we come first or second but that we have to qualify in whatever way we can. But let me reiterate we still have the confidence to do that. We've just got to accept the group standings as they are today.
"It doesn't mean that we are out of it. We've just got to make sure that we get through at the end."
Chelsea should have gone further ahead in the 55th minute when Drogba raced down the right and Frank Lampard passed the ball on to the unmarked Andriy Shevchenko, who shot over the bar with only the goalkeeper to beat.
Valdes rescued Barcelona with a double save in the 68th minute - blocking a shot from Drogba and then diving at the feet of Essien to smother his followup shot.
Messi almost equalized with six minutes to go but his header from a right-wing cross just went over the crossbar.
Champions of England and Spain the past two seasons, the two powerhouse clubs have met in this competition three years in a row.
Chelsea ousted Barcelona in the first knockout round two seasons ago and the outcome was reversed last term when the Spanish club won at Stamford Bridge on the way to capturing the title.
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