Drogba's recent form has propelled Guus Hiddink's side into the Champions League semi-finals as well as providing a three-team Premier League title race and it was the Ivory Coast forward who was once again the hero with an 84th minute winner.
Despite an array of attacking talent on show in front of 88,000 spectators, the match was unspectacular throughout on an unreliable and bobbly Wembley surface.
And rather than the brilliance of Drogba, Nicolas Anelka, Cesc Fabregas or Robin van Persie, the game will be remembered for defensive errors, none-more-so than from second-choice Arsenal goalkeeper Lukasz Fabianski.
The Poland international goalkeeper could be considered to be at fault for both Chelsea goals, while his under-performing opposite number Petr Cech was rarely put under pressure.
The first half was slow as both sides appeared to look nervous. But it was the Gunners who had the upper hand for long periods as they looked to get in behind the Chelsea rearguard.
However, the first chance of the half fell to Chelsea. From a high, hopeful ball, Fabianski rushed out of his area but mis-timed his run and Drogba plucked the ball out of the air to head goalwards. It was down to youngster Kieran Gibbs to clear the ball off the line.
Arsenal's first real chance provided the first goal of the game on 18 minutes.
Emmanuel Adebayor played Gibbs into the left-hand channel and the full-back was free to cross to Theo Walcott who volleyed home as the ball took a deflection off the hand of Ashley Cole to evade Cech.
Florent Malouda drew the sides level just after the half-hour. From a long Frank Lampard pass, the French winger skipped inside Emmanuel Eboue and hit a shot towards the near-post which Fabianski should have saved.
Minutes later, Nicolas Anelka saw his shot crash against the post after robbing Denilson of possession inside his own area.
The second half was absent of many clear-cut chances as both teams resisted throwing too many bodies forward.
As Arsenal began to tire, Drogba struck from another chance out of the blue.
From a lobbed Lampard ball inside his own half, Drogba ran clear of the Arsenal defence to control the ball and then round the onrushing Fabianski who was caught in no man's land, letting the Premier League's in-form striker tap home into an empty net.