They had their chances on this occasion, not least in the opening few minutes when both Marouane Chamakh and Laurent Koscielny squandered clear opportunities to land an early blow.
But still they lack the killer instinct that divides the great from the good; that, for years now at Arsenal, has been the reason why the team which so often plays the best football in this country is not the best team.
As Ray Wilkins admitted afterwards, it was a battle for Chelsea at Stamford Bridge.
A game when they had to work tirelessly just to gain time on the ball. But they did what was necessary, with Didier Drogba and Alex scoring the goals that extended this era of dominance over their London rivals.
Since the arrival of Jose Mourinho in 2004, Chelsea have lost just twice to Wenger’s men; under Avram Grant and Luiz Felipe Scolari.
Drogba has a remarkable record against them. Yesterday was his 13th goal in as many matches and his 10th victory in the same number of encounters without defeat.
In Sebastien Squi l laci and Koscielny, Arsenal had two centrehalves who certainly struggled to cope with that devastating combination of power and finesse that ranks Drogba among the top two or three strikers in the world.
While it was Alex who produced something truly spectacular with a free-kick straight from the Roberto Carlos repertoire, Drogba produced a trademark finish that once again demonstrated his impressive ability to score when travelling at speed.
From the delightful ball forward by Ramires to the cross from Ashley Cole, it was a swiftly executed move. And it was all the more memorable for the way Drogba took the left-foot shot in his stride and beat Lukasz Fabianski via his near post.
That goal arrived in the 39th minute, by which time Arsenal might have celebrated one or two goals of their own. Chamakh should have done better with a Bacary Sagna cross that he diverted wide with a close-range header, as should Koscielny when he somehow missed from inside the six-yard box.
Arsenal were playing some delightful stuff, with Jack Wilshere once again showing a watching Fabio Capello that the senior international stage is one he could comfortably occupy.
A fine opportunity soon fell to Andrey Arshavin, who forced the save of the afternoon from Petr Cech with a well-struck shot. But with the sight of Drobga’s opener came the sense that Arsenal simply could not match Chelsea for strength and power.
That there is something to be said for the fact Chelsea top the scales as the Premier League’s biggest team while Arsenal, so say certain statistics, are the smallest.
Anyone passing Chelsea’s dressing room after the match would have thought them giants, although that would have been because of the seven NBA stars – Kobe Bryant among them – who dropped in to congratulate them.
An Arsenal side boasting eight French-born players mustered little in response. Chamakh might have struck had he not hesitated when receiving a cross from Arshavin but the better of the second half chances fell to Chelsea.
Having done the hard part in first stealing the ball off Squillaci and then rounding Fabianski, Nicolas Anelka contrived to shoot wide of an empty goal and into the sidenetting. Michael Essien allowed Fabianski to make what amounted to a decent save when he, too, should have scored.
But from Alex came the moment of the match. An absolute missile of a free-kick that curled away from the diving Fabianski and flew into the roof of the net. A free-kick that has to rank among the fastest any goalkeeper will face.
That it came as a result of Koscielny’s reckless challenge on Anelka would have frustrated Wenger – as would the fact, of course, that this defeat comes after losing to West Brom the previous week.
Carlo Ancelotti’s side suffered a similar setback, albeit away to a Manchester City team now sitting second in the Premier League.
That the same team which lost at Eastlands also won here would have pleased Ancelotti. A point proved. But the more significant point was made to Arsenal who, for all their ability, have failed to heed the warnings of previous seasons. Their team remains a work in progress rather than the finished article.
Wenger has said they are ready and in fairness to Arsenal’s manager they came to Stamford Bridge without Cesc Fabregas and Robin van Persie. But it should say something to Wenger when Wilshere is his best player.
It should say that, for all the genius that is sometimes evident in the feet of players like Arshavin and Samir Nasri, they still need to take a step up the next level. It is why Chelsea have a gold badge and Arsenal do not.