Craig Beattie grabbed a last-minute equaliser at Somerset Park to deny us our first League 1 victory since August.
Alan Forrest gave Ayr the lead early in the second half but two superb strikes from Steven Doris had us on course for full points until Beattie, on as a substitute, popped up at the end.
The result means we remain eight points behind both Ayr and Stenhousemuir as we prepare to welcome Morton to Forthbank on Saturday.
Binos boss Stuart McLaren made one change from the team that lost 2-1 to Forfar the previous week, with James Creaney replacing Ross Forsyth. Darren Lee Smith and Lewis Coult were again out injured and Willie Robertson was absent due to illness.
U20 players Sean Robertson and Stephen Al-Sayed were named among the substitutes for our first visit to Somerset Park since a 3-1 defeat in April 2009.
Ayr had Andy Millen in caretaker charge following the departure on Monday of manager Mark Roberts following a run of five straight defeats in League 1.
Albion played some good stuff in the first half but clear-cut chances were at a premium and neither keeper was seriously tested – Callum Reidford saved a header from a corner and Gordon Smith dragged a shot wide at the other end.
Ayr went ahead in 54 minutes when Forrest, brother of Celtic player James, burst through the middle and rounded Reidford to knock the ball into the empty net.
The equaliser came midway through the second period when Doris found the top corner with a free-kick from 25 yards after Cunningham had been fouled and he netted his sixth goal of the season with another fabulous finish with 10 minutes left.
Substitute Graham Weir provided the assist and the ex-Dundee and Arbroath forward guided the ball into the bottom corner with a perfectly-placed shot that was wide of keeper David Hutton and just inside the post.
Stirling looked set to claim a vital win but the Honest Men, without a home victory since August, earned a point in the last minute when a free-kick from the left touchline was hoisted into the box – the ball was turned into the path of the unmarked Beattie and the former Scotland striker finished confidently with a first-time shot.
Ayr United: Hutton, Devlin, Crawford, Murphy, Cummins, Gilmour (Beattie 75), Forrest, McLaughlin, Donnelly, McGovern, Donald.
Subs (not used): Shirkie, Muir, McArthur, McGill, Newman (GK).
Goals: Forrest 54, Beattie 90
Stirling Albion: Reidford, Hamilton, Creaney, Beith, McGeachie, C Smith, Johnston (Weir 65), Comrie, Doris, G Smith (Small 65), Cunningham.
Subs (not used): Wedderburn, Fulton, Al-Sayed, McClune, Robertson (GK).
Goals: Doris 66, 80
Referee: John McKendrick