But they are putting a smile on the face of Carlo Ancelotti and their team-mates by developing an understanding so scarily good, they have become almost telepathic.
The duo made life hell for Bolton as they get ready for tougher tests that lay head in the next week.
Chelsea fans might not have found a song for manager Ancelotti like they did Jose Mourinho and Claudio Ranieri, but he knows how to make the moody two tick.
Make players like Drogba and Anelka feel like they matter and, judging by this masterclass, the end result is likely to be the Premier League title.
Ancelotti might look like a maths teacher in a blazer and jumper, but he has got his sums right on these strikers, praising them in public and I dare say even more in private.
Chelsea go into the most important week of their season so far in irresistible form after a performance that stuck two fingers up at the critics who rubbished them after away defeats at Aston Villa and Wigan
Don't believe that? Just ask Bolton Wanderers, who more than played their part but were no match.
Wanderers were even given a standing ovation by their fans at the end despite being smashed for four by Chelsea for the second time in a week.
Bolton's resistance even lasted until Frank Lampard's penalty in first-half stoppage time, a flashpoint that saw Jlloyd Samuel dismissed.
Ancelotti's bravehearts go to Atletico Madrid on Tuesday looking to seal a place in the knockout phase of the Champions League, with Drogba back after a three-match Euro ban.
Then next Sunday comes the battle for the undisputed Premier League heavyweight championship when they entertain Manchester United.
If this is anything to go by, Rio Ferdinand had better regain his form quickly or risk utter humiliation at the feet of Drogba and Anelka.
Poor Wanderers took such a battering in the first 20 minutes they deserve an open top bus ride for weathering the onslaught.
Just when Gary Megson's men threatened to get back into the game, they were dealt a cruel blow when Samuel tripped Drogba in the box.
The Ivory Coast hitman was about to pull the trigger and surely fire past keeper Jussi Jaaskelainen when he was tripped and Lampard made no mistake from the penalty spot.
Bolton felt the damage was done when ref Peter Walton brandished a red card in the direction of the Bolton full-back for upending Drogba.
The decision made Drogba and Walton about as popular with Bolton fans as Somalian pirates with world naval forces right now.
On this occasion the bloke in the black didn't deserve the abuse, following the letter of the law because Samuel was the last man.
Moments like this are when officials should be allowed to use common sense instead of a rule book that becomes more baffling than a MPs' expenses form.
Had Walton done what he most probably wanted to and dish out a booking, he may have been relegated to officiating at Accrington Stanley's next game.
Chelsea - who have now won seven on the bounce at Bolton without conceding a goal - were sensational in the second half.
Even if Samuel hadn't been dismissed, Bolton would never have coped with their skill, commitment and work rate.
People say Anelka is selfish, but just after the hour mark he showed his generous side by picking out Deco, who took his tally for the season to three when he slotted from just inside the box.
Bolton were doing little wrong, though, and Jaaskelainen was keeping the score down with a string of breathtaking saves.
The inevitable third goal followed in the 83rd minute when Zat Knight, under pressure from the mightily impressive Branislav Ivanovic, headed into his own goal.

But Ancelotti's amazing free scorers, who have banged 13 goals in a week, saved the very best for the last minute of the game.
Deco chested the ball in the path of Lampard, whose sublime back-heel was converted by Drogba.
That took the Ivory Coast markman's goals total for the campaign into double figures.
It could have been even worse for the home side but for Jaaskelainen's saves, the bar denying Lampard and Ivanovic having a strike ruled offside.
Yet after surviving the early siege, Bolton could have been two up before Lampard's fifth goal of the season.
Anelka has always rated his former team-mate Kevin Davies, who did the donkey work for him during his goal- laden two-year spell at the Reebok.
Davies, an honest bruiser, has perhaps been let down by his lack of goals and that might have cost him an England cap or two.
And Chelsea's players must have wondered what 'Le Sulk' was on about when Davies was put through by Johan Elmander but drove his left-foot shot wide.
Swede Elmander, whose Bolton career has been hampered by a hamstring injury, owes his club a goal or 10 and should have done better with his own effort inside the box.
Only five teams leading the Premier League at the start of November have gone on to win the title in 17 years. Don't bet against Chelsea beating the hoodoo.
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