County secured all three points, despite having played 120 minutes of football in midweek and being down to 10 men for the last six minutes of this match.
Airdrie have been ravaged by injury and struggled to cope with the energy of the visitors.
In the fourth minute a cross from County's Alex Burke fell just behind and out of range of the in-running David Winters.
However, within a minute, County opened the scoring. A Charlie Adam corner to the far post was met by Martin Canning, whose powerful header looped over Mark McGeown and into the net.
Airdrie displayed a lack of symmetry in their build-up and too often were wrong footed and outgunned in midfield.
But minutes before half time the home side were awarded a soft penalty when Owen Coyle was dumped in the box by Mark McCulloch. Stephen McKeown converted expertly from the spot.
Shortly after the restart County underlined their superiority with a stunning goal which started with Burke's run down the wing. Leaving Airdrie's trialist in his slipstream, Burke crossed into the box and set up an easy chance for Winters.
With nine minutes to go County's Steven McGarry was sent off for elbowing Airdrie sub Neil McGowan in the face. The decision met with derision from other County players, and Jamie McCunnie was cautioned for dissent.