The Gunners were ahead inside seven minutes when Mesut Ozil shrugged off his recent criticism to slot a low ball past Everton goalkeeper Joel Robles.
Everton, though, rallied and went into the break level following a fine counter-attack down the right by Ross Barkley, which ended up with Romelu Lukaku bundling home from close range.
Arsenal - who head to Bayern Munich next week looking to overturn a 2-0 deficit in the second leg of their Champions League last 16 clash - regrouped following the start and went back ahead when former Everton midfielder Mikel Arteta converted a penalty, which had to be retaken following encroachment.
Giroud, who had come on for Yaya Sanogo just after the hour, made sure with a late double, the second following a sublime passing move from the resurgent Gunners.
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 despatched 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 Barclays Premier League draw against with Everton in early December.
The Gunners continued to poor forward as Alex 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 number two 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 Gareth Barry after cutting inside.
Arteta smashed home the spot-kick into the bottom left corner - only for referee 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.
Source : PA
Source: PA