Gary Twigg gave the Diamonds an early lead only for County to hit back with goals from John Rankin and David Winters before the break.
Just when it looked as if County might add to their lead, Airdrie equalised 17 minutes from the end when Willie McLaren finished off a set piece.
Airdrie took a shock lead in the eighth minute when Twigg latched on to a precision pass from Stephen McKeown to drill the ball low past Stuart Garden.
County were getting plenty of the ball but attack after attack was breaking down in the last third of the park as Airdrie looked to hit on the break.
The home side had a great chance to draw level in the 29th when Winters chested down a Don Cowie delivery but the County striker hesitated and his shot was blocked.
That seemed to give County the impetus they needed and after their best spell in the game Rankin equalised in the 36th minute when he hooked in a another Cowie cross.
County kept up the momentum and Winters executed a neat turn and shot from outside the box that Stephen Robertson held comfortably.
But the home side got their noses in front a couple of minutes from the break when a Lionel Djebi-Zadie cross from the left was touched on by Steve McGarry and Winters drilled the ball home from 12 yards.
There were chances at both ends at the start of the second half. Cowie skimmed the bar with a header from a Winters cross then Kevin Barkey dragged his show wide of target after the County defence got themselves in a tangle.
County had another chance when Martin Canning just got under a Winters corner and the ball flew wide of target, then Robertson touched a long-range effort from Burke on to the post.
But the Diamonds got themselves back on level terms in the 73rd minute when an Allan McManus free-kick was flicked into the path of McLaren who picked his spot behind Garden.
County substitute Maciej Nuckowski came close in the final minute with a flashing shot that just cleared the bar.