The Ivory Coast forward scored both goals inside 23 minutes, and Chelsea then successfully contained Arsenal at Stamford Bridge.
For all their intricate play, the third-place Gunners lacked a cutting edge, just like last Sunday when they were dismantled by another title rival, Manchester United.
United is now two points behind Chelsea after briefly returning to the top Saturday by routing Portsmouth 5-0.
Chelsea, though, immediately bounced back from its surprise draw midweek at relegation-threatened Hull. Even the attempts by Arsenal fans to unsettle John Terry, who was sacked as England captain on Friday, failed as their chants were drowned out by the Chelsea faithful.
The Chelsea captain managed to evade the attention of the Arsenal defence in the eighth minute when the home side went ahead.
Terry ran through unmarked to flick on Florent Malouda's corner for Drogba at the far post to finish from close range.
Arsenal manager Arsene Wenger was furious, kicking his coat on the touchline and being reprimanded by the fourth official.
The Frenchman became more incensed when Arsenal squandered a golden chance to level in the 17th minute. Cesc Fabregas floated a cross over Ricardo Carvalho to Andrei Arshavin, but the Russia forward's volley was blocked by Petr Cech with his left boot.
There was a growing threat from Arsenal, but as the visitors pushed forward they left themselves exposed and were caught on the counterattack when Frank Lampard charged forward with the ball from inside his own half before slipping the ball through to Drogba.
The Ivory Coast forward cut inside and then smashed the ball past Manuel Almunia with his left foot to score his 12th goal in 10 matches against Arsenal.
Arsenal continued to have lots of possession, but Cech never looked seriously threatened. Fabregas shot wide and Gael Clichy missed the target from 30m before halftime.
Drogba almost completed his hat trick late in the game but his free kick crashed against the crossbar.
Chelsea extended its unbeaten home run to 24 matches, last losing at Stamford Bridge to Arsenal in November 2008.
Chelsea's win would appear to have put the Premier League title out of reach for Arsenal.
Wenger's side had put themselves back in contention by clawing back an 11-point deficit after a 3-0 home loss to Chelsea in November, and even had a brief spell at the top of the standings.
Now the north London club needs to beat a rejuvenated Liverpool on Wednesday to prevent the fourth-place team moving to within two points of third.
