Roberto Martinez's men started strongly and were rewarded in the 14th minute when Romelu Lukaku's shot was saved by Wojciech Szczesny and Steven Naismith fired in the rebound.
Lukaku added a second with an excellent run and finish after 34 minutes, and Arsenal's chances of a fightback were effectively extinguished in the 62nd minute when former Everton midfielder Mikel Arteta turned the ball into his own net under pressure from Kevin Mirallas.
There was one bright spot for Arsenal when Aaron Ramsey returned to action as a substitute following a lengthy injury absence, but it was the Everton fans who were able to celebrate long before the final whistle as they sealed a sixth straight win to boost their UEFA Champions League hopes.
Martinez's tactics saw him switch to 4-3-3 with Lukaku unusually stationed on the right wing to target Nacho Monreal, who was replacing injured left-back Kieran Gibbs.
Leon Osman, who had looped Everton's first shot of the match just past Wojciech Szczesny's left-hand post, got in a tangle with Bacary Sagna, resulting in a gash that opened up after appearing to catch a boot in the face.
It forced Osman's immediate exit down the tunnel after just nine minutes, but brought Ross Barkley to the fore in a more disciplined role on the left than he has been used to playing under Martinez.
However, with Gareth Barry providing support behind, the 20-year-old was still able to express himself and was instantly installed as the focal point of Everton's attacking play.
The goal, however, came from Arsenal's inability - or unwillingness - to engage opponents. Leighton Baines was allowed to carry the ball 30 yards into enemy territory unchallenged and with that amount of time he picked out Lukaku with a low cross. Although the Belgium striker was denied by Szczesny, Naismith was in the right place at the right time to ram home the rebound.
One Barkley through-ball caused panic in Arsenal's defence but Mirallas could only shoot weakly, while another sent Baines away down the left to create a chance for James McCarthy.
Martinez's ploy to expose Monreal down the other flank saw the Gunners defender give up the chase with Lukaku and call for Szczesny to race out of his area and clear.
Barkley continued to torment the visitors and after numerous step-overs hit an angled shot that was kept out by the goalkeeper's legs, with Mirallas also forcing a save near down at the same right-hand post.
Arsenal were cut open again just after the half-hour when Everton sliced their way through central midfield, with Naismith and Mirallas combining to release Lukaku on the right. Again Monreal, Thomas Vermaelen and Per Mertesacker stood off as he cut inside and the striker took full advantage to smash home left-footed.
Lukaku's celebration with Martinez on the touchline spoke volumes about the way the players have so wholeheartedly embraced the Spaniard's change in philosophy since replacing David Moyes in the summer.
The closest Arsenal came to a first-half reply saw Howard superbly tip over Lukas Podolski's dipping half-volley, but there was little else to enthuse over.
Everton, on the other hand, were rampant and midway through the second half applied the killer blow.
Mirallas broke from deep and although Szczesny just got to the ball before Naismith, it rebounded back in front of goal where former Toffees midfielder Arteta, under pressure from Mirallas, turned it into his own net.
Substitute Alex Oxlade-Chamberlain's shot against the crossbar late on seemed merely like Arsenal raging against the dying of the light.