The striker fired home from an early corner after John Terry had glanced a header towards goal, and his second came after a rampaging counterattack which saw Drogba smash the ball home on his left foot.
That opening 25-minute salvo was enough for the home side to take all three points, despite the dominance of possession that ArsÃƒÂ¨ne WengerÃ¢â‚¬â„¢s side experienced.
Arsenal now face a do or die meeting with Liverpool on Wednesday, with their hopes of ending their six-year wait for the Premier League title hanging by a thread.
The away side are currently in the midst of a pivotal part of their season, and knew anything short of a win at Stamford Bridge, after a defeat the previous weekend against Manchester United, would further disrupt their title chances.
But WengerÃ¢â‚¬â„¢s side started where they left off against the reigning champions and conceded within eight minutes.
John Terry, fresh from being stripped of the England captaincy, saw his flicked header drift wide of goal, but not before Drogba latched onto the loose ball, to tap home from two yards.
The former England skipper had dominated the front and back pages of last weekÃ¢â‚¬â„¢s newspapers, but after this latest assist he was sure to be mentioned in dispatches for all the right reasons as he helped Chelsea storm into an early lead.
The visitors did however show the sort of character that they had been devoid of at the Emirates a week ago, with Petr Cech equal to Andrey ArshavinÃ¢â‚¬â„¢s volley after Cesc FabregasÃ¢â‚¬â„¢ lofted pass.
But ArsenalÃ¢â‚¬â„¢s gung-ho attitude so early on in the game contributed to their downfall as The Blues doubled their lead on the counter attack. Frank Lampard eventually found Drogba and the Ivorian cut inside Gael Clichy before belting the ball past Almunia in emphatic fashion.
The second goal clearly dampened the visitorÃ¢â‚¬â„¢s spirits, and the slick passing game weÃ¢â‚¬â„¢d seen in the early stages was nothing more than a distant memory, with FabregasÃ¢â‚¬â„¢ dismal 40-yard effort which sailed harmlessly wide summing up the north Londoners’ predicament.
The early stages of the second half saw much of the same with Arsenal frustrated by a stubborn home defence. Even when clean through on goal Samir Nasri couldnÃ¢â‚¬â„¢t produce a strike with Ashley Cole valiantly blocking the FrenchmanÃ¢â‚¬â„¢s break.
Fabregas was able to make Cech work however with a curling effort from a close-range free kick, which the keeper brilliantly kept out.
But where a brilliant save thwarted Fabregas, the woodwork frustrated Drogba after a 30-yard strike rebounded off the bar with Almunia rooted to the spot.
It would have been DrogbaÃ¢â‚¬â„¢s first hat trick against Arsenal and the perfect way to wrap up a convincing win over their title rivals in similar fashion to the corresponding fixture at the Emirates in November.
But the former Marseille forward had to contend with just two on this particular afternoon, as Chelsea powered to the summit of the Premier League table and left Arsenal in disarray for the second week in succession.
Chelsea: Cech, Ivanovic, Cavalho, Terry, Cole, Ballack (Zhirkov 82), Mikel, Lampard, Anelka (J.Cole 87), Drogba (Kalou 90), Malouda
Unused Substitutes: Hilario, Ferreira, Alex, Deco,
Arsenal: Almunia, Sagna (Eboue 74), Gallas, Vermaelen, Clichy, Diaby (Rosicky 74), Song, Fabregas, Walcott (Bendtner 64), Arshavin, Nasri
Unused Substitutes: Fabianski, Campbell, Ramsey, Denilson
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