Kilmarnock's performance was less than impressive and, despite advancing to the next round, they will have to improve significantly if they are to have any chance against Celtic.
For much of the first half Airdrie matched their SPL opponents and looked assured at the back as Killie probed unsuccessfully.
With chances at both end's Killie were first to threaten and only a brilliant close-range save from Stephen Robertson, playing his 100th game for Airdrie, kept a Frazer Wright header out.
Stuart Noble sent top scorer Alan Russell on a great run into the box ,however the close attention of Garry Hay was enough to put the striker off.
Airdrie continued to pressure the Killie defence and after ten minutes they almost broke through. Paul Lovering slipped a tight pass into Noble whose turn and shot were expertly parried by the visitors' understudy goalkeeper South African Chad Harpur.
The end to end play continued until the 25th minute when Killie opened the scoring with a bizarre goal. Having conceded a free-kick some 25 yards out wide right the players crowded around the box waiting from the anticipated high ball.
Instead and whether by design or not, William Gibson drilled a low effort into the box. The mass of players all missed the ball and the keeper too and to the incredulity of all, the ball rolled into the net.
The loss of such a goal was hard to recover from and as Airdrie sought to regain their composure, Killie sought to extend their lead. The visitors won that battle and after 36 minutes went two up.
A pass into the box forced Stephen McKenna into a reckless challenge on Colin Nish and the referee blew for a penalty. Airdrie offered no protests and Nish took the kick and buried the ball in the back of the net.
The second half was by comparison a non-event until in the last quarter chances fell to both sides.
However, before that Airdrie were reduced to ten men when Darren Smith picked up two yellow cards in the space of six minutes.
Russell came close to reducing the deficit when four minutes from time he rattled an 18-yard drive off the underside off the bar.
Then on the stroke of full-time Gary Wales was prevented from scoring when his ten-yard diagonal shot was brilliantly saved by Robertson.