Danny Welbeck gave the Gunners an early lead and full debutant Alex Iwobi doubled their advantage just before half-time, as Arsenal easily outplayed the hosts in the first half.
Everton improved slightly after the break, but they never truly troubled the Gunners, who move within just three points of Spurs following the win.
As reported by Arsenal's official Twitter account, manager Arsene Wenger handed Iwobi a chance to start ahead of Olivier Giroud and Theo Walcott. John Stones and Gerard Deulofeu started on the bench for the Toffees:
Everton had a positive start to the match, as Seamus Coleman immediately burst forward down the wing and registered the first shot after a corner, but their momentum quickly faded as Arsenal took over.
Welbeck hit the post after just three minutes, and the England international underlined his strong form with a run that resulted in a corner, which fell to Gabriel Paulista. The Brazilian couldn't get his effort on target, but it was clear momentum was shifting in favour of the visitors.
The Gunners' passing was crisp and put tremendous pressure on the Everton defence, and after just seven minutes, it led to the first goal. Alexis Sanchez found Welbeck, who used his speed to create a chance before slotting home with ease.
Per WhoScored.com, Arsenal have really missed his presence in the squad:
Iwobi nearly made it 2-0 soon after, with Sanchez servicing the youngster, but his side-footed finish lacked any power and didn't trouble goalkeeper Joel Robles.
Everton seemed to lack any sort of creativity and resorted to lobbing the ball in the direction of Romelu Lukaku, who found himself completely isolated against the Arsenal defence. Meanwhile, the Gunners found plenty of success on the counter-attack, and Mesut Ozil came close to adding a second goal, as his shot came off Phil Jagielka for a corner.
David Ospina produced a fine stop to deny Muhamed Besic, who fired Everton's best chance of the half too close to the stopper, but apart from that, the Toffees produced few chances of note. And as the first half wore on, the Gunners again increased the tempo, looking for a second goal.
Sanchez wanted a penalty after 35 minutes, after Besic appeared to make contact inside the box. ESPN FC's Mike Goodman thought the Chilean had a case:
A number of crosses failed to hit the target for Arsenal, but a defensive error saw them score a second goal just before half-time. Hector Bellerin did well to set up Iwobi, who was given far too much space to take aim and fire home a goal on his first-ever Premier League start.
BBC Sport's Phil McNulty thought it was yet another example of Everton's defensive struggles:
Welbeck nearly made it 3-0, just missing the target after a wonderful attack, before official Mark Clattenburg whistled for half-time.
Arsenal continued their strong attacking play early in the second half, but a handful of passing moves didn't lead to any immediate chances. Stones, who had replaced Besic at half-time, nearly handed Welbeck a second goal on a platter, but he raced back to fix his error just in time.
Bleacher Report's James McNicholas was stunned by how poor the home side looked:
Francis Coquelin tried his luck with an optimistic shot from long range, firing it well over the crossbar, but apart from that chance, the Gunners seemed content to drop the pace of the match a bit.
Coleman was one of the few Everton players who seemed willing and capable of changing his side's fortunes, but when he went on another impressive run before firing a cross into an empty Arsenal box, it summed up just how little support he got from his team-mates.
Ospina appeared to suffer a serious injury after an accidental clash with Lukaku, and while the goalkeeper could seemingly hardly move after receiving some medical attention, Wenger decided against taking him off.
FIFA Digital's Alex Stone couldn't believe he stayed on the pitch:
Jagielka fired a header inches over almost immediately after, having beaten the hobbled Ospina to the ball. Gabriel then made sure his stopper didn't have to make a save from Tom Cleverley's strike, as Everton suddenly started finding some openings.
Ozil was the next Gunner to pick up a knock after Stones accidentally stepped on his heel, but he left the pitch under his own strength and will have the chance to heal up during the international break.
Giroud was furious after Clattenburg missed an off-the-ball incident, where Ramiro Funes Mori seemed to trip up Frenchman. Per Paddy Power, studio analyst Howard Webb thought the Argentinian deserved a booking for his troubles:
Arsenal fans had even more reasons to be annoyed with Clattenburg just minutes later, as he blew his whistle for a foul on Jagielka just as Giroud had the ball in the back of the net.
It had no impact on the final score, however, as Arsenal held on for the win, despite a late chance for Lukaku, who put Ospina to work one last time.
Injured Arsenal goalkeeper Petr Cech praised his team-mates for their strong showing:
Scorer Iwobi was happy to get his name on the board in his very first start, but he thought the win was far more important, per the Premier League's official Twitter account:
The youngster seemed to have an excellent understanding with Welbeck from the opening kick, so look for him to receive plenty more chances to impress in the coming weeks.