A 69th-minute strike from Leandro Trossard secured three points for Mikel Arteta’s side, after their last win on home soil against Manchester United before the international break.
The Belgium international sent the away fans into a bedlam as he struck with a well-calculated left footed effort, after receiving a cut pass from Saka.
Earlier in the first half, Gabriel Martinelli curled a fine, right-footed finish into the bottom right corner of the Everton goalpost before it was ruled offside by the Video Assistant Referee.
Five minutes later, the Brazilian winger was forced off with and replaced by Trossard.
In the 32nd minute, new Arsenal goalkeeper, David Raya, made his debut as he stood to the challenge when he saved a low effort from Gueye.
Arsenal’s right back, Ben White, made a straight attempt at goal straight into the hands of Pickford after a neat one-two with Odegaard.
Three minutes after Nketiah made way for Jesus, the Gunners had their goal, courtesy of substitute Trossard.
As the Toffees ran out of time, the home fans continued to yearn for more.
Leading the Arsenal attack line was Nketiah who started ahead of Gabriel Jesus, despite scoring a fabulous goal against United.
Mikel Arteta made a significant change in the starting lineup as Havertz made way for Pablo Vieira in the starting lineup.
The Gunners occupy the fourth position on the English Premier League table having secured 13 points from their first five matches.
Everton remain in the relegation zone with just a point.