The Gunners had been second best on home soil up until two goals just before the hour mark gave them complete control of the match.
Alexandre Lacazette opened the scoring with a curled finish into the top corner, three minutes before Pierre-Emerick Aubameyang finished off a good team move to add three more points to the home side's tally.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Cech; Bellerin, Mustafi, Sokratis, Monreal; Torreira, Xhaka; Ramsey, Ozil, Aubameyang; Lacazette
SUBS: Leno, Holding, Lichtsteiner, Guendouzi, Elneny, Iwobi, Welbeck
STARTING XI: Pickford; Kenny, Zouma, Keane, Digne; Gueye, Davies; Walcott, Sigurdsson, Richarlison; Calvert-Lewin
SUBS: Stekelenburg, Holgate, Baines, Bernard, Schneiderlin, Lookman, Tosun
Unai Emery: "We've won two matches away and that's small progress, but very important for continuing to improve our confidence. I think we are finding the balance. Now it's very important, and our objective, to improve in the defensive moments."
Marco Silva: "Of course the second goal was one moment with Jordan [Pickford] but the other two, we have to do better in that situation like we prepared. It's something we analysed during the week. They already know what we did in the wrong way and what I expect in the next game that we don't do the same."
ARSENAL SUBS: Leno, Lichtsteiner, Guendouzi, Elneny, Iwobi, Welbeck
EVERTON SUBS: Stekelenburg, Holgate, Baines, Bernard, Schneiderlin, Lookman, Tosun