Airdire took an early lead when Stephen McDougall headed home from close range after Stephen McKenna had flicked on a corner from the left after just four minutes. With 15 minutes gone, Iain Anderson fired high and wide of the target in a rare Dundee attack .
William McLaren went close to scoring Airdrie's second, but with Kelvin Jack beaten, his curling left foot shot flew just past the post.
Ten minutes before half-time, Iain Anderson sent a looping header over Lee Hollis, but his effort went inches past the post. Minutes later Adrian Madaschi couldn't control the ball when unmarked six yards from goal giving Airdrie time to clear the danger.
A Barry Smith effort from just inside the box was well blocked by Neil McGowan with an hour gone.
Simon Lynch was denied his seventh Dundee goal by a great save by Lee Hollis, who turned his low shot around the post in the 68th minute.
Fifteen minutes from time Bryan Prunty doubled Airdrie's lead when he fired past Kelvin Jack from six yards after being set up by Brian McPhee.
McPhee himself sent a header crashing off the post from close range with eight minutes played.