Drogba, who has scored 12 goals in as many appearances against Arsenal since joining Chelsea in 2004, was left unmarked at the far post and simply poked home captain John Terry's header from a Florent Malouda corner in the eighth minute.
His second came on the break after some sustained pressure from Arsenal, when England midfielder Frank Lampard burst out of his half in the 23rd minute, galloped 20 metres and laid the ball off to the Ivorian on the right of the Arsenal area. The big striker stepped inside Gael Clichy to ram the ball past a stranded Manuel Almunia.
The result, following a 3-1 defeat at home by Manchester United last weekend, leaves Arsenal nine points adrift of Chelsea and seven behind the champions.
Before the goal Chelsea keeper Petr Cech had had to make two saves in quick succession, diverting a ball at Samir Nasri's feet behind for a corner and blocking a shot from Andrei Arshavin with his feet as Arsenal used the speed of Nasri, Theo Walcott and the tricky Russian to harass the Chelsea defence.
But Arsene Wenger's team, so energetic in the build up, lacked the final flourish.
They failed to capitalise on a free-kick just outside the area in the 69th minute after subsititute Nicklas Bendtner was brought down by Ricardo Carvalho, Cech pulling off a fine double save. Despite constant moves down the wings, they could not find a way through a defence stubbornly marshalled by Terry.
The Chelsea captain showed no sign of strain despite being stripped of the England captaincy on Friday following a week of lurid press headlines about alleged extra-marital affairs, including one with the former girlfriend of England team mate Wayne Bridge.
"My captain has a fantastic attitude. He's done very well every game for the team," Chelsea coach Carlo Ancelotti told reporters.
"It's very important to have this leadership."
SUBDUED WENGER
Arsenal coach Arsene Wenger praised Terry's defensive qualities.
"I give credit to Chelsea for their defending. They have fantastic defenders. I believe John Terry wants to win every time he plays football. Sometimes playing can be a diversion from events off the pitch," he said.
Almost every touch of the ball by Terry was greeted with boos from Arsenal fans and cheers from the Chelsea support. The 29-year-old flung his shirt into the Chelsea crowd after applauding them following the final whistle.
Wenger watched mostly stony-faced as his side's title chances ebbed. Arsenal have not won the league since 2004 and last captured silverware with the FA Cup in 2005.
"Against Manchester United we did not turn up. Here, we were completely dominant," he said.
"I always thought we would come back but you have to give them credit, they defended very well. There were lots of tricks from a very experienced team."
Arsenal were the last side to beat Chelsea at home, in November 2008, under last-but-one Chelsea coach Luis Felipe Scolari.
Since then Chelsea, under tem
