Jim Jefferies' side had chances early on but it was Keigan Parker who opened the scoring after 28 minutes when he curled a free-kick past Ryan Scully to put Airdrie in front.
Dunfermline had plenty of possession but did not really threaten and Airdrie made sure of victory in the final minute when Jim Lister netted his eighth goal of the season after a mix-up in the Dunfermline defence.
Ayr United's play-off hopes suffered a setback when they lost 2-1 away to Brechin City.
Robert Thomson scored his seventh goal of the campaign after six minutes and Craig Molloy made it 2-0 in the second half. Alan Forrest pulled a goal back for Ayr with 15 minutes left but Brechin held on.
Stranraer, also in the play-off hunt, came from behind to draw 1-1 with East Fife at New Bayview.
Nathan Austin put East Fife in front with a header midway through the first half. Stranraer hit back and Scott Robertson equalised after 77 minutes to salvage a valuable point.
Stenhousemuir twice came from behind to earn a point in a 2-2 draw with Arbroath at Ochilview. Paul McManus opened the scoring for Arbroath after half-an-hour but Ben Greenhalgh pulled Stenhousemuir level before half-time.
Bobby Linn netted for the bottom club late on but Sean Higgins equalised with his 10th goal of the season with only four minutes remaining.