Paddy Boyle gave Airdrie a fourth-minute lead but Michael Moffat struck twice in six minutes to put Ayr in front. Nathan Blockley hit back to equalise before half-time.
Ayr defender Gordon Pope was dismissed after 51 minutes for denying a goalscoring opportunity but David Hutton saved Willie McLaren's penalty.
Winger Alan Forrest joined Pope in the dressing room four minutes later but Moffat went close to completing his hat-trick.
Dunfermline Athletic came from behind to beat Stranraer 3-1 at East End Park. Martin Grehan gave Stranraer the lead midway through the first half after Ryan Scully had saved Chris Aitken's penalty but Andy Geggan equalised soon afterwards and Luke Johnston and 19-year-old Allan Smith scored late on.
Lee Erwin netted twice as Arbroath saw off Brechin City 2-1 at Gayfield. Bobby Barr scored a consolation.
Stenhousemuir won 2-1 away to Forfar Athletic with Sean Higgins and Darren Smith on target. Iain Campbell's pulled one back with a late penalty.