Jamie Adams gave Ayr the half-time lead but Isaac Layne equalised in the 47th minute to rescue a point for the bottom-placed side.
Dunfermline missed the chance to take over Ayr after being held to a goalless draw by sixth-placed Peterhead.
Airdrieonians came out on top in the day's most exciting match. Airdrie raced into a three-goal lead within the first 30 minutes but narrowly held onto the lead after Forfar Athletic's Scott Martin scored twice to bring them to within a goal of their opponents.
Stenhousemuir moved up to fifth in the table after a goal in either half from Mark Gilhaney and Jason Scotland gave them the victory over Stranraer. Ryan Thomson scored a consolation for Stranraer in the 92nd minute.
Results in full (half-time scores in brackets): Albion Rovers P-P Cowdenbeath, Brechin City 1-1 Ayr United (0-1), Dunfermline 0-0 Peterhead (0-0), Forfar Athletic 2-3 Airdrieonians (1-3), Stranraer 1-2 Stenhousemuir (0-1)