As Rafa Benitez knows to his cost, it's unwise to add any more fire to the belly of the Ivory Coast powerhouse.
Because Drogba did more than a lot in this victory that could well signal the end of Arsenal's title chances.
He scored twice in the first half, taking his tally against the Gunners to an incredible 12 in his last 10 games, and only the bar denied him a hat-trick.
With John Terry shutting out the media storm about his personal life to help keep things tight at the back, there was more than a sense of predictability about the outcome at Stamford Bridge.
Not that an attack led by Russian lightweight Andrey Arshavin was ever going to really knock one of the world's most resolute defences out of their stride.
The little forward is an exceptional talent but understandably finds the going tough as the centre-forward up against two colossal defenders.
Criticising Arsenal would be easy after their comprehensive defeat last week against Manchester United but this was a better performance.
The Gunners had more of the play for long spells but had no sting to go with all their pretty football.
And that's a pretty familiar tale when they come up against the Chelseas and Manchester Uniteds.
It took only eight minutes for Chelsea to expose their London rivals' frailties and, inevitably, Terry was involved. The Blues skipper headed a Florent Malouda corner goalwards and Drogba tapped in at the far post. Both were criminally unmarked.
Wenger's side didn't let it knock them out of their stride and, after Petr Cech managed to deny Samir Nasri when out of position, the keeper was forced to pull off an important save to keep out an Arshavin volley.
But, on 23 minutes, it all seemed too easy for the home side. As Carlo Ancelotti had predicted in his press conference on Friday, one of the keys to beating Arsenal is to hit them on the break.
When Arshavin was dispossessed, it soon became four versus four and Frank Lampard timed his pass to perfection to find Drogba in plenty of space on the right.
The single-minded striker was only going to do one thing. Bear down on goal, cut in and wallop a left-footed shot past an unprotected Manuel Almunia.
Job done.
The visiting fans couldn't look when arch-enemy Ashley Cole appeared to be in on goal for a third but Theo Walcott raced back to distract the England full-back and keep his team in the game - just.
Arsenal had enough of the ball to suggest they could find a route to goal but it never really happened for them.
Instead, Chelsea carried a threat on their attacks with Lampard's flick lacking power and Michael Ballack firing across the face of goal.

A big moment at the other end around the hour mark saw Ashley Cole produce a saving challenge as Nasri seemed likely to score and Cech made one outstanding stop to keep out Cesc Fabregas' free-kick.
Cech also had to scoop the ball away from substitute Nicklas Bendtner from a Fabregas header but the closest we came to another goal was when Drogba hit a peach of a free-kick against the woodwork with Almunia standing and admiring the effort as it rattled his crossbar.
There was then a telling moment as Fabregas fouled Drogba and seemed to indicate to referee Mike Dean that, due to the size difference between the two stars, there was nothing else he could do to halt the African.
It was a metaphor for the whole contest and, football being a ruthless game, Dean simply showed the yellow card to the Spaniard.
Nicolas Anelka should have added a third against his former club when lashing wastefully off target when again left totally unmarked from a Lampard free-kick although Fabregas sent a header wide at the other end as time ran out.
Fabregas took another hefty knock in the process, as Branislav Ivanovic crunched into him, and his frustration was clear for all to see.
He did his utmost, as did his team-mates, but they were muscled out of things by the powerful Premier League leaders. Even with his thigh injured and heavily strapped after being clattered by Cech, Terry soldiered on with his customary resolve and determination to lead from the front.
Chelsea have regained the lead in the title race and Arsenal are now nine points adrift.
While all the talk for the past fortnight has been about Terry and his off-the-field misdemeanours, this afternoon was all about Drogba and his systematic torture of the Gunners.
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This article has 14 comments
Drogba is the best striker in the world. period!!
By Ayoola Ojo.. Posted February 9 2010 at 4:10 PM.
I thinks wenger want profit than trophy that is why he don;t to buy mature players remember he is prof in economics.
By Tawiah Francis.. Posted February 9 2010 at 7:46 AM.
It is obvious now that Arsene needs to seriously work on the psychology of play of these young lads,are their legs so weighty that they can not shoot? Even when on one-on-one with the goalie,there must be a pass,one wonders if they are afraid to score.Arsene is stupidly stubborn,and he's loosing it,l am beginning to think him too old--fashioned!
By Fash.. Posted February 8 2010 at 5:47 PM.
As long as Wenger remains the head coach at arsenal nothing can be won. He started digging his grave four years ago by selling Viera, Pires, Wiltord,Kanu, Lauren, Gilberto, Henry,Flamini,Toure without replacing them with quality players. Arsenal now is quantity as against quality. What pains me most is after tutoring these players for some years, he would sell them cheaply. So my club has become a selling club. I"ll recommend that he be redeploy to arsenal feeder team since he's in love with the teenagers while a coach like Guus Hiddink, Maurinho or Ruud Gullit be employed at the end of the season.
By Dele Akande.. Posted February 8 2010 at 5:02 PM.
DROGBA IS ONE AMAZING PLAYER HE SCORED 2 FANTASTIC GOALS YESTERDAY I SAW THE GAME AT MY FRIENDS PLACE HE JUST BELTED THEM IN IM GLAD HE.S WITH CHELSEA AND NOT WITH ANY OTHER FOOTBALL CLUBS AND I HOPE HE DOESN.T GO ANYWHERE CHELSEA CERTAINLY DO NEED HIM IF I EVER SEE DROGBA IM A CHELSEA FAN IM GOING TO SHAKE HIS HAND AND SAY THANKS TO 2 AMAZING GOALS FROM LOUISE CROYDON
By louise.. Posted February 8 2010 at 4:16 PM.
I completely agree with your opinion but they're still losing the games.
By Anourian.. Posted February 8 2010 at 3:56 PM.
same old same old when will this idiot wenger be told we need more class in our team we got thrashed last november what did wenger do go on the good run we had beating teams lower than us when it comes to chelsea man spew we can not beat them another season with no trophy git beaten by man u home and away in cl feel so angry well done wenger you are letting te fans down big time o more excuses
By jade.. Posted February 8 2010 at 2:12 PM.
chelsea is my choice and is the best club to me in and if chelsea meat arsenal at 100 times arsenal will be suffering
By akinsanmi sola.. Posted February 8 2010 at 12:17 PM.
Can any Arsenal fan tell me what Wenger sees in "52 chances" Bentner and "erratic final pass" Eboue.
When both are on the pitch Arsenal are playing with 9 men.
2-0 down against Chelsea both were put on the pitch ! No chance !
This has been going on for at least the last 3 years
Why hasn't Wenger bought a world class striker; goalkeeper; defender ?
Is it because he's not interested in winning anything ?
Is saving money his priority ?
What about the fans paying high membership and travel expenses!
No wonder Fabregas wants to leave !
By John Barry ailing Arsenal Fan.. Posted February 8 2010 at 11:22 AM.
i think its one thing understanding a mistake and learning from it.arsenal never seem to be in position to do either of the two.the counter attack for chelsea's 2nd reminds me of man u's 2nd goal 4 man u against the gunners the previous weekend.is arsenal a team that is learning something or its just mediocre talk?arsene,wont u learn something?
By martyn m.. Posted February 8 2010 at 7:07 AM.
Arsenal will never win the title again as long as wenger stays and plays with kids.....
By noname.. Posted February 8 2010 at 12:04 AM.
Chelsea is a better team.We are the best.
By Lovelace.. Posted February 7 2010 at 7:41 PM.
I have said for the past 2 years
"52 chances" Bendtner if on the pitch Arsenal are playing with 10 men.
"erratic final pass" Eboue if both are on the pitch Arsenal are playing with 9 men.
That's exactly what happened today 2-0 down to Chelsea.
Why hasn't Wenger bought a new World class striker, and a Goalkeeper and possibly a defender,
What do other Arsenal fns think.
By john barry arsenal fan.. Posted February 7 2010 at 7:26 PM.
Being a Chelsea fan, very happy with the result, however I think the best football was played by the Arsenal.
By Mark s.. Posted February 7 2010 at 7:08 PM.