Olivier Giroud, who missed several chances as the Gunners slumped to a 3-1 home defeat by Monaco in the first leg of their Champions League last-16 clash on Wednesday, netted a fine volley on 39 minutes to put Arsenal ahead on Sunday.
Substitute Tomas Rosicky then scored a late deflected effort to eventually settle what was at times a nervy encounter
Everton, impressive winners of their Europa Le ague tie against Young Boys on Thursday night, had plenty of possession, but could not find a way past David Ospina, who made a fine point-blank save from Romelu Lukaku
Despite their shortcoming in Europe, Arsene Wenger's men remain in good domestic form, as a third successive league win moved them ahead of Manchester United and are now just four points behind Manchester City following their defeat at Liverpool.
With Danny Welbeck and Theo Walcott both left on the bench - along with defender Per Mertesacker as Gabriel Paulista made his first Premier League start - there was not a lot of width about the Arsenal side.
Lukaku, who scored twice on Thursday night, was again the main focal point for the visitors.
In the 17th minute, the Belgian forward capitalised on a hesitation by Gabriel as the Brazilian was caught in two minds whether to head a long ball up field back to the goalkeeper or hack clear.
Colombian Ospina, again preferred to Wojciech Szczesny, showed no such deliberation as he raced out to meet the bouncing ball, palming it away before then making a sliding tackle on Lukaku as he moved wide.
Arsenal continued to probe with some short passes, and eventually created an opening down the left on 28 minutes.
Santi Cazorla, who captained the side, exchanged a one-two with Mesut Ozil before moving the ball out to Alexis Sanchez
The diminutive Chilean clipped the ball through a crowded six-yard box, where Giroud dived in with a brave header to nod the ball just wide as Everton captain Phil Jagielka closed in.
Gabriel, signed from Villarreal in the January transfer window, made a superbly-timed sliding tackle to halt Lukaka as the Everton forward charged into the Arsenal penalty area following another dangerous break.
Arsenal took the lead on 39 minutes.
Ozil whipped in a corner from the right, and Gabriel's run to the near post opened space for Giroud in the six-yard box
The France striker got ahead of his marker to guide the ball into the far corner.
The Gunners continued to press ahead of half-time, and Everton goalkeeper Tim Howard touched over a dipping 20-yard effort from Cazorla.
Everton, who find themselves in the bottom half of the table, made a positive start after the break as Gareth Barry sent a volley over.
Giroud saw his close-range effort cannon off the arm of Jagielka as the Everton skipper made an important block while on the ground before the France striker played a clever one-two with Cazorla at the edge of the Everton box, and the Spaniard sent a rising drive just over
On 64 minutes, Ospina produced a superb reflex save to turn over Lukaku's near-post drive at point-blank range.
There was a lengthy stoppage after a clash of heads between Giroud and team-mate Francis Coquelin, leaving the midfielder with blood pouring from his nose.
Ospina showed good reflects again after Seamus Coleman's low cross from the right was turned goalwards by Aaron Lennon, the former Tottenham winger on as a substitute.
Everton continued to show plenty of industry and were enjoying a spell of possession as the match headed into the closing 10 minutes.
Arsenal almost sealed it on the break, but Jagielka made a goal-saving block as Ozil looked to stab the ball into the far corner after being played in by Giroud.
The Everton captain, though, could then only help a low strike from Rosicky fly past his own keeper as Arsenal eventually made sure of all three points in the final minute, before some seven added on for stoppages.
Source : PA
Source: PA