It was a breathless, end-to-end tie of high quality that was nowhere near as one-sided as the eventual scoreline may have made it appear, two goals in the final seven minutes from Olivier Giroud adding a flattering gloss for Arsenal.
Arsenal took the lead in the seventh minute as Santi Cazorla capitalized on a slip by James McCarthy and laid in Mesut Oezil, who slid a calm finish past Joel Robles.
Robles, looking insecure throughout, pushed a Bacary Sagna cross against the bar as Arsenal continued to press, but Everton levelled on 32 minutes.
Gareth Barry intercepted and set Ross Barkley away down the right. His low cross found Kevin Mirallas at the back post and his miskick flipped the ball over Lukasz Fabianksi for Romelu Lukaku, who controlled the ball and tapped in from close range.
But midway through the second half, Alex Oxlade-Chamberlain stumbled over the challenge of Gareth Barry in the box and Arteta converted the penalty, showing admirable nerve after being asked to retake his initial effort because Giroud had encroached.
And with seven minutes remaining, Giroud made the game safe, slamming in Bacary Sagna's cut-back after a clever ball from Tomas Rosicky.Two minutes later, Giroud had his second, rolling in after Rosicky and Oezil had shredded Everton on the break.
The other three quarter-finals, including Manchester City against holders Wigan Athletic, take place on Sunday.