Arsenal progressed to the last four of the FA Cup at the first time of asking but not without a fight against an Everton team who gave as good as they got at the Emirates.
Mesut Ozil scored his first goal of 2014 - and his first since the last time Arsenal played Everton in December - after seven minutes, but Everton deservedly equalised on 32 minutes when Romelu Lukaku tapped in from close range after a swift counter-attack.
However, the match was decided midway through the second half as Gareth Barry was wrong-footed in the box by Alex Oxlade-Chamberlain and tripped the Arsenal man. Mikel Arteta stepped up against his former club to score the penalty, only to be forced to retake it due to encroachment by Olivier Giroud.
Arteta changed the location of his penalty on the retake, going high and right instead of low and left, but it produced the same outcome.
Giroud then sealed the match with eight minutes remaining by turning in a low cross from close range, before doubling his tally shortly after.
It means Arsenal reach the FA Cup semi-finals for the first time in five seasons and just the second time since winning the competition in 2005.
Everton made a bright start in the early Spring sunshine, but Arsenal took the lead. Santi Cazorla broke from midfield and to the edge of the visitors' penalty area, where he fed Ozil. The German playmaker took his shot first time on his left foot and dispatched a low strike into the bottom right corner.
It was a much-needed confidence boost for the £42.5million midfielder, who had been given a rest by Wenger, was jeered by some German supporters when in action over the international break and had not scored since the 1-1 Premier League draw against with Everton in early December.
The Gunners continued to pour forward as Oxlade-Chamberlain's effort was parried by Spanish goalkeeper Joel.
At the other end, Bacary Sagna blocked Steven Pienaar's shot before another quick Arsenal break ended when Ozil's effort was charged down by John Stones, the 19-year-old defender again standing in for injured captain Phil Jagielka.
Everton's back-up goalkeeper was then almost caught out by a cross from Sagna through the six-yard box, which he tipped onto the crossbar as it looped over his head.
Everton were level on 32 minutes. A superb break down the right from Barkley saw the ball chipped right through the Arsenal six-yard box. Kevin Mirallas' scuffed shot saw the ball drop back into the centre, where Lukaku was on hand to bundle it over the line.
Arsenal had rarely looked in any danger until that point, and were soon back on the offensive as a 20-yard drive from Oxlade-Chamberlain was parried by Joel before Cazorla's volley was deflected behind.
Everton were almost gifted another goal early in the second half when a slip from captain Thomas Vermaelen, back in the side after a hamstring problem for Laurent Koscielny, put Lukaku away on the right.
The Belgian surged forward and then laid the ball back for Barkley, but the England midfielder could only crash his shot over the bar - much to the frustration of the 5,000-strong Everton fans in the Clock End.
Arsenal were awarded a penalty on 67 minutes when Ozil's backheel released Oxlade-Chamberlain down the right and he was tripped by Barry after cutting inside.
Arteta smashed home the spot-kick into the bottom left corner - only for referee Mark Clattenburg to order a retake for encroachment by Giroud. The former Everton midfielder kept his nerve to fire the ball past Joel again, this time high into the right side of the net.
With the tie having opened up, both sides made changes as Aiden McGeady and Leon Osman came on for Everton as Oxlade-Chamberlain made way for Tomas Rosicky, who earlier this week signed a contract extension with Arsenal.
Arsenal secured their semi-final trip to Wembley when Sagna got away down the right and to the goalline, where he cut the ball back for Giroud to crash home a third on 83 minutes.
Arsenal, though, saved the best for last as a blistering counter-attack ripped Everton apart. Cazorla fed Rosicky down the right, who in turn picked out Ozil, and his first-time ball into the centre was swept home by Giroud to keep Arsenal on course for a first trophy since 2005.