Drogba scored his 13th goal in 13 appearances against Arsenal to widen the gap at the top of the Premier League to four points, and now find themselves seven ahead of today's opponents.
Carlo Ancelotti kept faith with the same team that lost to Manchester City last weekend, no doubt keeping in mind that they have steam-rolled all others that have faced them beforehand.
Arsene Wenger, meanwhile, gave Jack Wilshere another chance to show everyone how he is maturing into a fine footballer, with Lukasz Fabianski still deputising for the injured Manuel Almunia.
An absolutely blistering start to the game saw Arsenal twice come within a whisker of a goal within the opening two minutes.
First Marouane Chamakh got ahead of John Terry inside the penalty area to connect with Bacary Sagna’s cross to attack the ball but his headed chance flicked off the boot of Alex and went inches wide. Then, from the resulting corner, Laurent Koscielny found himself unmarked two yards out but seemed as surprised as the Chelsea defenders and managed to head the ball over.
Terry nearly made amends for his previous lack of concentration but putting Florent Malouda through with a fantastic long ball and it was Sebastien Squillaci’s turn to dawdle as Malouda ran inside him to control the ball but with the ball failing to sit up properly for the Frenchman, his effort rose over Lukasz Fabianski and over the bar.
Now with their own tails up Chelsea again broke with Michael Essien, Didier Drogba and Nicolas Anelka all combining with a wonderful one-touch charge on Arsenal’s goal, but it ended with Sagna conceding a corner.
Despite the end-to-end nature of the game, it was not until mid-way through the first half that either keeper was properly tested. Arsenal worked the ball from right to left to Andrey Arshavin, who was lurking 25 yards from goal. The Russian took one touch and let fly with a stunning half-volley towards the far corner, only for Petr Cech to make an equally beautiful one-handed save.
Keeping up with the nature of the game, Chelsea immediately hit back with their own attempt to break the deadlock, and Fabianski was also equal to it. Essien fed Drogba down the left flank and the Ivorian galloped into the area and hit a stereotypically powerful shot towards the near post but the Arsenal goalkeeper was also equal to it, getting down low quickly as an open Ramires screamed at his teammate for not squaring the ball.
With Arsenal playing, arguably, their best football of the season so far, the last thing they needed was to concede to undo all their fine work but that is exactly what happened. Ramires did extremely well in the centre of the pitch winning two tackle and playing in Ashley Cole whose low whipped ball found Didier Drogba six yards out, but with the ball slightly behind him, the striker improvised beautifully to pirouette and backheel the ball off the near post and into the net for his 13th goal in 13th appearance against Arsenal.
Tempers visibly grew after the goal as first Malouda was lucky not to get booked with an over-the-ball challenge on Sagna then Essien appeared to tread directly on Abou Diaby’s ankle leaving the Arsenal midfielder in agony as the half-time whistle was blown.
Arsenal started the second half like they did the first, straight on the front foot. Jack Wilshere stabbed a ball down the side of the defence and Chamakh, who managed to untangle himself from Terry, got to the ball just before Cech. The goalkeeper brought the striker down but after Chamakh pushed the ball out of play. There was definite contact from Cech but the Moroccan went down a little too theatrically for a penalty to be given.
Minutes later and Arsenal had another shot for a penalty. Chamakh dummied Ramires and shaped to come inside, but Ramires just won the ball with his trailing leg was a desperate but fair challenge.
Again though, with Arsenal bossing possession it really should have been 2-0 when Anelka somehow managed to miss an open goal. The last man Squillaci found himself in plenty of space 35 yards from his own goal but his continual hesitation allowed Anelka to nick the ball off him before whizzing straight for goal. Fabianski came out but the exiled French international moved smoothly round him and then, from 12 yards, only managed to drag his shot into the side-netting at the near post.
Then Chelsea had the ball in the back of the net after a lovely move and pass from Anelka that resulted in Arsenal favourite Ashley Cole to slot home, but all celebration were over long before the net rippled as the linesman raised his flag to claim a close, but correct, offside decision.
The story of the first half mirrored the story of the second as Arsenal definitely enjoyed the majority of possession but were wasteful in front of goal, whereas Chelsea came much closer with any opportunity that fell to them as they stood firm in defence and waited for the counter-attack with Anelka again coming close with such a break but Fabianski saved well with his feet.
The match was finally decided with five minutes remaining in the only way it would be, a set piece. As Arsenal started to look tired in defence, they conceded a freekick about 25 yards out. Alex stepped up and absolutely thundered the ball into the top right-hand corner as the bar swerved left and right past the helpless Fabianski in goal.
As the final whistle blew minutes later, Arsenal now find themselves seven points behind today's victors, but if they can repeat the performance throughout the season they can be keep their heads high.