Chelsea leapfrogged Manchester United with 58 points compared to the Old Trafford club's 56, while Arsenal, whose title challenge is now in tatters, remain nine points behind the Blues on the 49-mark.
Both sides started at a high tempo which resulted in numerous mis-placed passes.
But it was the scourge of Arsenal who broke the deadlock on eight minutes in the game's first worthwhile attack on goal.
Ivory Coast hitman Drogba tucked home a simple tap-in from two yards after Florent Malouda's in-swinging corner was headed on by the under-fire John Terry.
Arsenal almost levelled on 16 minutes but Petr Cech, who was playing his 250th game for the Blues, smothered a shot from Samir Nasri.
Cech was forced into a brilliant save from Andrey Arshavin seconds later.
With Arsenal attacking, Chelsea countered quickly on 23 minutes and Lampard bulldozed his way through the middle of the park before passing the ball to Drogba on the left.
The striker crashed through the Arsenal rearguard before cutting into a central position in the penalty area.
He then left fly an unstoppable left footer past the hapless Manuel Almunia to double the scoring for the home side.
Lampard almost scored with a cheeky back heel from six yards on 55 minutes after excellent set-up play by Drogba and Malouda but Almunia was quick to spot it.
A magnificent last-ditch tackle by Ashley Cole inside the Chelsea penalty on 60 minutes prevented Nasri from getting a clear shot on target.
Gunners boss Arsene Wenger replaced ineffectual Theo Walcott with Nicklas Bendtner on 64 minutes.
A fantastic save by Cech on 68 minutes thwarted Cesc Fabregas' pinpoint free-kick from just outside the penalty area.
With seven minutes remaining, a sensational free-kick by Drogba from 20 yards rattled the Arsenal crossbar with Almunia rooted to the spot.
This followed an intense period of Arsenal possession but Chelsea successfully saw out the remaining minutes of the game.