Strikers Steven Naismith and Romelu Lukaku both scored for Everton in the first half, while Arsenal midfielder Mikel Arteta added a third with an own-goal in the second period in a match the home side dominated.
The result meant fifth-placed Everton closed the gap on Arsene Wenger's side in fourth place to just a single point, and the Toffees also have a Premier League game in hand over their London rivals.
Everton manager Roberto Martinez handed Naismith, who impressed from the bench against Fulham last time out, a place in the starting line-up ahead of Ross Barkley while Kevin Mirallas was preferred to Gerard Deulofeu.
Arsenal had Aaron Ramsey back in their squad for the first time since December after his recovery from a thigh injury but he had to settle for a place among the substitutes while Nacho Monreal started in place of Kieran Gibbs, who had an ankle injury, at left-back.
Leon Osman signalled Everton's intent and went close with a curling effort from distance, which had Arsenal goalkeeper Wojciech Szczesny worried, that just went over the crossbar.
Osman, named Everton captain for the day, was forced off moments later with a nasty cut on his face after Arsenal defender Bacary Sagna landed on him and was replaced by Barkley.
But despite his absence the Toffees zipped the ball about with confidence and a slick move in the 14th minute allowed Naismith to put the hosts ahead.
A teasing ball into the area from left-back Leighton Baines found Lukaku who saw his shot from near the penalty spot parried by Szczesny, but Naismith was quickest to react and confidently placed the ball into the corner of the unguarded net.
Everton's pressure on the Arsenal goal was relentless and Barkley drew a smart save on the half-hour mark from Szczesny before Mirallas had the Poland international scrambling across his goal shortly afterwards with a low shot from distance.
Arsenal's rearguard was eventually breached for a second time by on-loan Chelsea striker Lukaku who notched his 12th Premier League goal of the season in the 34th minute.
The Belgium international received a cross-field pass on the right flank and skipped past Arsenal defenders Monreal and Thomas Vermaelen before he struck a powerful shot into the corner.
Arsenal briefly flickered into life before the interval and Lukas Podolski's shot was acrobatically tipped over the crossbar by Tim Howard in the Everton goal.
Wenger's side began the second period in a determined fashion but Everton simply matched them and their desire was reflected in the manner of the third goal shortly after the hour mark.
Mirallas stole possession off Sagna on the halfway line and headed towards the Arsenal goal where he found Naismith with an intelligent pass.
Naismith saw his path to goal blocked by Szczesny, but the ball popped free and Mirallas, who had continued his run into the penalty area, battled Arteta - a former Everton player - in the scramble which ultimately saw the Arsenal midfielder inadvertently push it into his own net.
From that point there was no way back for Arsenal although a run from Alex Oxlade-Chamberlain, introduced for Podolski in the 66th minute, saw him rattle the crossbar with a spectacular effort.
But it was Everton who finished the stronger of the two sides with Barkley, Baines and substitutes Deulofeu and Aiden McGeady all threatening with runs into the box.
Arsenal have their season ruined through injuries- Walcott, Ramsey and Ozil are the long absentees while many have been injured for a while too.
