The fourth round tie between the sides first and second in the Premier League was not quite the thrilling sideshow many had hoped for, but one which highlighted the Blues' strength in depth.
Cesar Azpilicueta and Juan Mata came in from the cold to net either side of half-time in a 2-0 Chelsea win - a result which means Wenger has now failed to overcome Mourinho in all their nine meetings.
The last encounter before this was the 2007 League Cup final, which the west Londoners won during a time in which the managers' relationship was far more fractious.
Those differences appear to have diminished over a time, with Mourinho's ire in the build-up instead focusing on the schedulers.
Initially threatening to field Chelsea's under-21 development side in protest of the match being little over 48 hours after the league clash with Manchester City, he eventually backed down in respect to Chelsea's fans.
The Portuguese still made 10 changes to Sunday's 2-1 win but all of those introduced were senior internationals, who were backed vociferously from the outset by 9,000 travelling fans.
Those supporters, like on Sunday, were grateful to a defensive mistake from their opponents. This time Carl Jenkinson was at fault, with Azpilicueta latching onto his poor back header to prod home midway through the first half.
Nacho Monreal almost levelled immediately and Aaron Ramsey came close on a number of occasions early in the second half, only for Chelsea to ensure the repeat of the final six years ago would go the same way.
Mata, still yet to prove himself indispensable to Mourinho, controlled the ball on the edge of the box and took a touch before unleashing a venomous right-footed strike, booking Chelsea's place in the fifth round.
The opening stages were lively enough but lacked clear-cut chances, with both defences quick to stop building danger.
A blocked Samuel Eto'o effort in the opening seconds was the best Chelsea could muster until the 19th minute, when Kevin de Bruyne managed to test Lukasz Fabianski for the first time.
Six minutes later they had the lead, pouring forward after an Arsenal corner with a massively deflected ball from Michael Essien causing confusion in the Gunners defence.
Despite Jack Wilshere being well placed to clear, Jenkinson chose to head back to Fabianski - a move Azpilicueta read, beating the Arsenal goalkeeper to the ball to poke home.
The right-back was clearly, and understandably, devastated by the mistake, which fellow full-back Monreal almost wiped out moments later.
Nicklas Bendtner's pressure forced goalscorer Azpilicueta to give the ball straight to Monreal, whose fierce left-footed strike whistled just wide of the far post.
It was the closest either side came as the first half came to a close, with a horribly sliced Essien strike only noteworthy due to how bad it was.
Eto'o whistled a strike just wide shortly after the sides reemerged, although it was Arsenal that had the better of the early stages.
Santi Cazorla swung an effort wide from the edge of the box, before Ramsey wriggled free to hit a strike that took a deflection and bobbled just wide.
The Wales international hit a right-footed strike just wide in the 63rd minute as Arsenal continued to press, before Wenger brought on Mesut Ozil, nominated for the FIFA Ballon d'Or earlier in the day.
Despite his introduction, Arsenal's chances were soon all but ended by another world-class performer.
Meeting the ball on the edge of the box, Mata rifled home into the top corner in front of the Chelsea fans who had packed out the Clock End.
Substitute Olivier Giroud forced Mark Schwarzer into a save at his near post soon after his introduction, but the Gunners were still looking susceptible at the back.
Ramires almost took advantage when he burst down the right and pulled back for Eto'o, who bundled his close-range effort just wide.
Wilshere fired over and Cazorla put wide as Arsenal looked for a late consolation that never came.
Instead, Ramires saw an effort land on the roof of the net in stoppage time and, perhaps feeling sorry for the hosts, referee Phil Dowd did not even book Thomas Vermaelen for hauling down Demba Ba when last man. David Luiz also came close in the latter stages.