Dundee went close on 15 minutes when a great cross-field ball by Barry Smith found Steven Craig wide on the left, but his lofted shot towards the far post went just over.
The home team went ahead on 21 minutes when Kevin McDonald played the ball to Craig O'Reilly 12 yards from goal and the big striker fired a low left foot shot into the corner of the net.
Stephen McDougall fired just wide for Airdrie Utd on 33 minutes.
Dundee doubled their lead on the stroke of half time when Robert Mann's 20-yard free kick sneaked in at Stephen Robertson's left-hand post. Airdrie United pulled a goal back in the 57th minute when Bryan Prunty lashed it home from close range after McDougall had knocked back Paul Lovering's cross.
Airdrie United substitute Brian McPhee crashed a 30-yard effort against the crossbar with nine minutes to go and seconds later Prunty's shot was saved by Kelvin Jack.
The visitors scored a deserved equaliser three minutes from time when Prunty scored his second and then amazingly two minutes later he completed his hat-trick again with a close-range effott both from Brian McPhee crosses.