The home side recovered from a goal down thanks to Tomi Adeloye's header three minutes into the second half after Lewis Smith had opened the scoring for the visitors five minutes before the break.
Adeloye squandered a number of chances to win the match for Ayr, who remain two points off the bottom of the cinch Championship.
Speaking to BBC Scotland, Adeloye said: "To get something out of the game is obviously a positive.
"We created enough chances and need to be more clinical, I take responsibility for that also. We just need to be more clinical."
Meanwhile, Airdrie’s cinch League One meeting with Queen’s Park has been postponed after a Covid outbreak at the Lanarkshire club.
The sides were scheduled to play on Saturday but Airdrie successfully applied for a postponement after being hit with a number of positive tests and related close contacts.