Arsene Wenger's men faced a stern test at Goodison Park with Everton losing only one of their last 15 games in all competitions.
The Londoners arrived on Merseyside after a disappointing draw on Boxing Day which saw Manchester United take top spot in the Premier League, while the Toffees were buoyant after beating Bolton 2-0 and consolidating their top six position.
Everton went ahead in the 19th minute as Mikel Arteta's wicked corner eluded everyone but Nicklas Bendtner on the line whose clearance only found the sole of Tim Cahill's right boot which nestled the ball in the back of the net.
It was no more than Everton deserved as the home side had took the game to the Gunners from the off with Yakubu holding the ball intelligently up front and Steven Pienaar, Tim Cahill and Arteta controlling the midfield.
It's very rare when Arsenal are given a footballing lesson but that is exactly what Everton were doing as Pienaar and Yakubu jinked and tricked their way around a defence that looked shell-shocked and quite frankly impotent.
Manuel Almunia's goal looked under threat time and again as corners were delivered with precision from Arteta, who seems to have found his form once again.
It was the sheer quality of Everton's build up play though which seemed to leave William Gallas, Bacary Sagna, Kolo Toure and co completely spellbound at times with Phil Neville almost repeating his Boxing Day scoring feat.
Tony Hibbert linked with Yakubu and Pienaar in the best move of the game to tee the captain up only for his 25-yard effort to sail over the bar.
The Gunners had a three-minute spell before half-time were they actually looked an attacking threat, but Wenger would have made his way to the dressing room with his work cut out.
Whatever he said worked as Arsenal were level practically from the kick off as Gael Clichy's long ball from well inside his own half hoodwinked Phil Jagielka and fell to Eduardo who slotted home from six yards.
It was a crushing blow to a stunned Everton and served to give the Gunners added impetus in the immediate aftermath.
Everton were not cowed though, indeed shortly after Yakubu should have put the Toffees ahead but his header went wide after connecting with a great cross from Joleon Lescott.
Everton immediately paid the price for the poor finish on 59 minutes as Eduardo eluded a falling Jagielka once again, collecting Bendtner's long header and putting Arsenal into the lead with the coolest of finishes.
In fairness to the Blues, they refused to stop battling and went forward in wave after wave, but unfortunately they lacked the same purpose and movement and Arsenal looked increasingly comfortable sitting on their lead and waiting to strike on the counter.
Andy Johnson replaced Hibbert on 69 minutes as David Moyes threw caution to the wind.
Bendtner then threw the Toffees a lifeline as he was dismissed for a scything tackle on Johnson.
Everton could have scored two in as many minutes as Arsenal's defence shook once again under the weight of blue shirts.
A horrible mix up between Joseph Yobo and Time Howard sealed the game for Wenger's side as sub Emmanuel Adebayor took full advantage of the latter's indecisiveness to nip in and slot home.
To add salt to the wounds, Arteta was sensationally sent off with five minutes to go as Cesc Fabregas made the most of the Spaniard's innocuous raised arm during a tackle, convincing referee Martin Atkinson he had been the victim of an elbow.
Substitute Tomas Rosicky's injury-time goal just compounded Everton's misery.