Jim Leishman's men took the lead in the 16th minute. It was set up by great play from Noel Hunt, who beat three Airdrie defenders before firing hard at goal. The Airdrie goalkeeper did well to block the shot, but could only watch as Gary Mason slammed home the rebound.
The Fifers doubled their advantage in the 23rd minute, but this time Airdrie only had themselves to blame. From a Lee Makel free-kick the defence got into a shambles and Hunt was left with an open goal from three yards.
The visitors scored the goal their play deserved on the half-hour as midfielder Stephen Docherty rose to head home a Stephen McKeown free-kick.
At the start of the second half Airdrie pulled level. Brian McPhee caused panic in the 51st minute as he ran at the home side's defence. He was able to slip the ball to midfielder Martin Hardie, who powered through to beat the keeper one-on-one.
Dunfermline pushed ahead again in the 56th minute and were lucky not to have their third goal from Derek Young ruled out for the challenge on Airdrie's goalkeeper.
Airdrie were given further hope as Pars playmaker Makel was sent off in the 62nd minute for a second bookable offence.
They laid siege to Dunfermline's goal, winning corner after corner as they searched for an equaliser.
It finally came right on 90 minutes from the penalty spot after a Dunfermline hand had blocked a shot on the line. McKeown converted the resulting penalty.
The grandstand finish that the away supporters desired came, and when Docherty headed home a Willie McLaren header, the seal was set on a sensational cup tie.