2 second half goals from Barkley and a Garbutt before a late scare from substitute Di Giacomo ensured Everton of a place in the final the next day against Partick Thistle who defeated Celtic 2-0.
Keeper Kenny Arthur returned to Glasgowâ€™s West End where he spent many happy years as a Jag as he watched as Ryan Donnelly headed over a Sean Lynch free kick.
The Toffeeâ€™s stepped it up a gear after the break. Arthur did well to deny John Lundstram before George Green blazed a shot over the bar.
But the opening goal was coming and it arrived in the 56th minute. Good footwork and a nice pass from Hallam Hope who found Ross Barkley who made no mistake.
On 63 minutes Everton increased their lead, Gavin Griffin handled on the edge of the box and from thr free kick Luke Garbuttâ€™s effort went in off the underside of the bar.
Garbutt became a villain when he conceded a penalty and from the spot kick Paul Di Giacomo made no mistake from the spot.
Team: Airdrie: Arthur, Hart, Griffin, McDonald, Kenneth, Lynch, Bain, Blockley, Boyle, Donnelly, Cook. Subs: Stallard, Lilley, Di Giacomo, Crawford, Duncan, Smith, Buchanan
Everton: Taudul, Browning, Garbutt, Lundstram, Hammar, Bidwell (c), Green, Barkley, McAleny, Hope (Forrester 85), Grant (Touray 75) Subs: Springthorpe(GK), Long, Jones
Match Officials Ref Mr D Roache Assistants Stephen Finnie & Stuart Hodge