The Ivory Coast striker slotted home deep into added time in the first half.
This contrast between this match and the thrilling if ultimately disastrous 1-1 semi-final second leg back in 2009 was a joy to behold.
That night scandalous referring decisions and players losing their tempers resulted in the Londoners missing out on the chance of appearing in the final.
Tonight was simply a titanic battle of wills and consummate concentration by the home side.
Barcelona had 72 per cent possession of the ball. The majority chances on goal. But Chelsea, to a man, produced a performance of their careers.
Petr Cech was the last line of defence and shielded his goal like a parent defending his offspring.
Frank Lampard rolled back the years to marshall the midfield which snuffed out mercurial Lionel Messi once again.
Up front, and on his own was Drogba. The man showed, when he stays on his feet, that he can be unplayable.
Tonight he was more nuisance than anything else but was on hand score the winner.
After just three minutes, a long ball by Mikel fell to Drogba in an advanced position but he failed to grasp the ball and it dribbled to Victor Valdes.
Nine minutes in and Barcelona should have scored when Alexis Sanchez broke free in the Blues penalty area but chipped the ball over Cech and saw it rebound off the crossbar to safety.
Seconds later and up the other end Gary Cahill found himself in the perfect position, eight yards out, but in the melee of players around him, failed to control the loose ball.
A Lionel Messi inspired move on 17 minutes saw him zip through the Chelsea rearguard to Cesc Fabregas arrowed the ball past Cech. Incredibly Sanchez appeared to get in front of the shot and claw it away from goal at the last moment.
With Daniel Alves charging freely down the right flank, it was inevitable he would get in a clean byline cross. This he did on 27 minutes and at the end of it was Messi who headed towards goal forcing Cech into a smart left hand diving save.
Ashley Cole came to the rescue with three minutes of the half remaining.
Once again, Messi, on a counter attack, sliced through Chelsea and passed the ball to Cesc Fabregas. His shot was on target but Cole responded quickest and hacked the ball before it crossed the line.
Deep into added time and against he run of play, the home side took the lead. With only three attacks worthy of the name, the Blues set off on a counter-attack of their own. Frank Lampard produced a fine reverse pass to Ramires on the left.
The Brazil midfielder raced into the left side of the Barcelona area before sending of a low left-footed cross. This time Drogba,not offside, met the ball comfortably and clipped the ball with his left foot past Valdes.
The second half started as the first with Barcelona running rings round the Londoners.
After just five minutes Adriano found himself in space just outside the Blues area. Cech was at his very best to parry away the fierce right-footed drive.
Quite how Sanchez failed to level the scores on 56 minutes will remain a mystery.
Scintillating approach play by the Spanish side saw Chile striker with the easiest of chances to tuck home from close range but he shot wide much to the relief of the Chelsea faithful.
Barcelona boss Josep Guardiola made his first change, bringing on Pedro Rodriguez for the off-form Sanchez on 65 minutes.
Ramires entered the ref's book three minutes later. Up stepped Xavi Hernandez to hack the free kick over the crossbar. The midfielder, no doubt feeling aggrieved then conspired to get a yellow for a needless foul a minute later.
Robbie Di Matteo then made his first change bringing on Salomon Kalou for Mata with 17 minutes remaining.
Guardiola responded by hauling off Fabregas for Thiago Alcantara five minutes later.
His final throw of he die came with six minutes to go off the bench came Issac Cuenca for Xavi.
The visitors almost scored immediately but Cech produced a fine save to deny the glancing header of Carles Puyol.
Di Matteo then took off Ramires for Jose Bosingwa on 88 minutes hoping to stem the incessant tide of Barcelona attacks.Chelsea's luck held during added time when Thiago's low curling shot rebounded off Cech's left upright and Busquets thumped the ball high goal the net.
The ref Felix Brych blew his whistle, the crowd and Chelsea players went delirious.
It's game on for the second leg on Tuesday with a prize of a visit to Munich for the winners now just 90 minutes away.