Goals from Mesut Ozil and Mikel Arteta and an Olivier Giroud brace sent the hosts through to the last four of the FA Cup.
Arsene Wenger's men scored three times in the last 22 minutes to move into the final four of a competition it last won in 2005.
|VIEW FROM EMIRATES STADIUM
|By James Goldman
A significant hurdle overcome for Arsenal who had to dig deep in order to defeat a spirited and talented Everton side who pushed the Gunners much closer than the final scoreline suggests. The game swung on the penalty won by Alex Oxlade-Chamberlain and converted by Mikel Arteta at the second time of asking.
That it came just minutes after Ross Barkley had blazed over the best chance of the game demonstrates how easily hopes of silverware can vanish in a split second. Arsenal have specialised in throwing away promising positions such as this in the past but are now just two steps away from getting the mother of all monkeys off their backs.
His last came in December’s 1-1 Premier League draw with Everton, but the Germany international showed no signs of rustiness as he finished with aplomb inside the area.
Despite the hosts enjoying much of the play from then on, Everton equalized just after the half-hour mark following a rapid breakaway.
Romelu Lukaku profited after good work from Ross Barkley and Kevin Mirallas — prodding home from close range to continue his scoring form since returning from injury.
Mikel Arteta restored the lead from the penalty spot in the 68th minute following Gareth Barry's clumsy trip on Alex Oxlade-Chamberlain before Olivier Giroud struck twice late to kill the game off.
It ended Roberto Martinez's hopes of becoming the first manager to win back-to-back FA Cups with different clubs as Everton's winless run at Arsenal in all competitions was extended to 20 matches.
Amid frantic opening exchanges, Ozil opened the scoring after just six minutes — keeping his cool to sidefoot Santi Cazorla's slipped pass into the far corner of Joel's net.
That knocked the wind out of Everton's sails somewhat, but the visitors almost equalized shortly after when Bacary Sagna blocked off Steven Piennar inside the area.
A nervous-looking Joel then tipped Sagna's center onto his crossbar as the Spaniard struggled to settle after a lively opening.
Going forward, Everton looked dangerous to a point but, more often than not, failed to find the killer final ball on the break.
However, it eventually got their counterattack strategy spot on as the lively Barkley scampered down the right and crossed for Mirallas at the far post.
The Belgian cut the ball back for countryman Lukaku, who had time to control before tapping home.
Barkley had the first chance of the second half, curling an effort over the crossbar after Thomas Vermaelen gave possession away cheaply to Lukaku.
Cazorla then forced Joel into a smart save to his left before Oxlade-Chamberlain went down under the challenge of Barry soon after the hour mark following some tricky footwork from the 20-year-old.
Former Everton man Arteta then put Arsenal back in front from the spot after seeing his first effort cancelled out due to encroachment from substitute Giroud.
It was Giroud himself who got on the score sheet seven minutes from time to settle any nerves before he finished off a quick break to move Arsenal within one game of the final.