Stirling were forced to settle for their fourth successive draw as 10-man Ayr hit back for a point.
Martin Glancy hit the crossbar for Stirling early on, while Paddy Connolly had a good chance saved for the visitors.
The deadlock was broken after 61 minutes when Glancy bundled the ball home after Scott McLean's deflected shot had been brilliantly saved by Ludovic Roy Three minutes later the visitors were reduced to 10 men when trialist Jimmy Doyle was sent off for a terrible tackle on McLean.
Dougie Wilson then missed a good chance for Stirling before McLean hit the inside of the post after being put through by Glancy.
But Ayr were not to be denied, and with 10 minutes left Andy Ferguson equalised with a low shot after poor defending from the home side.
Both sides had chances to win the game in the final minutes, but McLean sent a free-kick just wide for Stirling and Ayr substitute Scott Chaplain was denied by a goal-line clearance.
Albion have completed the first quarter of the campaign unbeaten, but Ayr will be happier with this result in what was the first league meeting between the sides since 1998.