The Gunners were poor in the first half but strikes from Alexandre Lacazette and Pierre-Emerick Aubameyang in the second period ensured the three points would go to Arsenal.
The Toffees created some good openings early on but were made to rue their chances.
Cech on form
There has been a lot of discussion about who should be starting in goal for Arsenal this season and after Bernd Leno started in the Europa League on Thursday, Petr Cech was back in the side and back in form against Everton.
Cech's footwork has been questionable this season but he was at his best with his hands to keep Arsenal in proceedings throughout the first half.
Dominic Calvert-Lewin should have scored after just two minutes for Everton as he was sent through on goal but Cech came out well to deny the young forward.
Arsenal's number one then made a similar save to keep out former Gunner Theo Walcott after he'd got beyond the defence later in the half.
Richarlison, back after suspension for the visitors, also forced Cech into action, the Czech keeper being on hand to stop him twice in a first half where Arsenal were very open at the back.
Unai Emery's team looked lacklustre in the first period, and there was no intensity to their play, something that was summed up by Nacho Monreal having the Gunners best and only opportunity of the first half after 12 minutes.
Aubameyang laid the ball into the full back at the back post after Hector Bellerin's cross but Jordan Pickford kept Monreal out.
Gunners spring to life
After half time the Arsenal attack finally found their rhythm and went two goals ahead just before the hour mark.
Lacazette had touched the ball just seven times in the first half but produced a fantastic finish 11 minutes into the second period. Aaron Ramsey found him just inside the area before the Frenchman got the ball out of his feet and curled home a brilliant opening goal.
Just minutes later Arsenal found themselves another goal, this time in rather less emphatic circumstances. Lacazette played Mesut Ozil into the acres of space on the right channel and the German found himself through on goal.
Rather than shooting he chose to play in Ramsey instead but he couldn't sort his feet out to find the net. However, the Welshman did find Aubameyang behind him who was left with a simple tap in.
The forward was in an offside position but it wasn't spotted by the officials.
Arsenal building momentum
The Gunners were far from their best but two finishes from their star forwards was enough to separate the two teams. Cech, however, still had to remain focused late on to ensure Arsenal kept their first clean sheet of the season.
He got down well to save from Michael Keane's header with just over 20 minutes remaining whilst he was also alive to Cenk Tosun's effort, beating it away to cap off a productive afternoon for the goalkeeper.
Arsenal hadn't created much and weren't convincing but it was a fifth win on the bounce for Emery's men in all competitions. Everton remain winless away at Arsenal in the Premier League era.