Arsene Wenger's side remain on course to finally end their nine-year trophy drought thanks to an enterprising quarter-final display in the spring sunshine in north London.
Mesut Ozil ended his three-month wait for a goal to give the hosts a perfect start before Romelu Lukaku's equaliser. Once Mikel Arteta had converted a penalty midway through the second half there was only ever going to be one winner, and France forward Giroud's late double ensured Arsenal can look forward to a last-four date at Wembley in April.
With Arsenal's UEFA Champions League hopes hanging by a slender thread - they travel to Bayern Munich on Tuesday trailing 2-0 from the first leg - and their Premier League title charge fading, the FA Cup could represent their best chance for silverware this season.
Everton boss Roberto Martinez is no stranger to glory in the competition having masterminded unfancied Wigan Athletic's FA Cup final win over Manchester City last season. But his bid to earn a repeat with Everton looked in trouble from the moment Germany midfielder Ozil slid home the seventh minute opener for Arsenal.
Santi Cazorla made the most of a slip by James McCarthy, and his perfectly-weighted pass ensured the out-of-form Ozil scored his first goal since December. Ironically, Ozil's last goal came against Everton and you could see his confidence lifted as well as that of his team-mates.
Arsenal were looking to expose stand-in Robles at every opportunity, but they were caught by a quick counter-attack that ended in Everton's 32nd minute equaliser. Ross Barkley broke through from midfield and even though Kevin Mirallas scuffed his shot from the cross, it fell kindly for on-loan Chelsea striker Lukaku to turn the ball home.
For all Arsenal's dominance at the start of the second half, Everton should have taken the lead in the 53rd minute through Barkley. A Thomas Vermaelen mistake was seized upon by Lukaku and his pass gave Barkley a clear sight of goal, only for the England midfielder to curl his shot past Fabianski's right-hand post.
In an increasingly tight game it appeared a mistake might prove the difference, and so it proved as Gareth Barry's clumsy trip on Oxlade-Chamberlain left referee Mark Clattenburg with no choice but to point to the spot. Arteta's first penalty was converted and, after Clattenburg ordered a retake for encroachment, the Spaniard stepped up to once again beat Robles in the 68th minute.
Then Giroud's two late goals finished it off as he poked home Sagna's 83rd-minute cross, before a quick-fire three-man attack was ended with the Frenchman tapping in two minutes later.