The win moves Mikel Arteta’s Arsenal side up to ninth place in the league and back in the battle for European places, while Everton remain without a win at the Gunners in 24 years.
Pierre-Emerick Aubameyang scored twice to earn Arsenal a 3-2 Premier League win over Everton on Sunday, extending the Gunners' unbeaten start to 2020 and moving them back into the battle for European places.
The win lifts Mikel Arteta's Arsenal side up to ninth place in the league with 37 points, while Everton remain without a victory at the Gunners in 24 years and a point adrift in 11th.
As well as the goals of the prolific Aubameyang, who is now joint top scorer in the league on 17 with Jamie Vardy, Arsenal had keeper Bernd Leno to thank for some late saves which preserved the lead.
Dominic Calvert-Lewin put Carlo Ancelotti's team ahead in the first minute with a superb, acrobatic volley after David Luiz had failed to deal with a Gylfi Sigurdsson free kick.
Yet Arsenal reacted well, with young forward Eddie Nketiah, who started ahead of Alexandre Lacazette, levelling in the 27th minute, his first goal at the Emirates coming from a fine cross from the left from substitute Bukayo Saka.
Six minutes later and Arsenal were ahead — Luiz making amends for his earlier mistake with a lovely, defence-splitting pass to Aubameyang who calmly slotted past Jordan Pickford.
Brazilian Richarlison brought Everton back on level terms though just before the interval, poking home from close range.
Arsenal, however, struck straight after the break with Aubameyang heading in a Nicolas Pepe cross, 23 seconds after the restart.
Leno then produced a brilliant point-blank reflex save from Calvert-Lewin and did well to keep out a Richarlison effort as Everton pushed for an equaliser.
Arsenal went close to a fourth goal when Nketiah, who spent the first half of the season on loan at Championship (second-tier) Leeds United, struck the bar with a curling shot.
Everton almost grabbed a point at the end but Calvert-Lewin's header from a Bernard cross went just wide.
The victory completed an excellent week for Arteta's side after their 4-0 Premier League win over Newcastle United and 1-0 win at Olympiakos in the Europa League on Thursday.
"The best thing is the spirit we showed after coming back from Europe - three games in seven days. And coming back after we went behind. The resilience they showed after they were absolutely shattered. Three wins in seven days, for sure it is my best week," said the Spaniard.
Ancelotti said his striker Calvert-Lewin was continuing to progress but needed to work on his focus.
"He is doing well but (it is) not enough. If he wants to be a top striker, he has to work more hard, focus hard, work more. He is doing well but he has to have the game to be focused all the time," he said.
"Defensively, we were terrible. We have to improve. There were three goals we could have avoided. It was too easy for Arsenal to score three goals.
"We had a lot of opportunities at the end of the game to equalise and we did not get it. We are working, we believe in what we are doing. Today was a step down. We need to refocus. We need to re-balance," said the Italian.