Stirling gave their play-off hopes a massive boost by claiming their tenth win in the last 12 league games to move to within a point of fourth-placed Peterhead.
Albion, beaten at Dumbarton last week, had to dig deep for victory as the visitors pressed hard after going behind, but they held on to move seven points clear of an Ayr team yet to win in 2006.
The decisive moment arrived five minutes after half-time when winger David O'Brien tumbled under a challenge from defender Martyn Campbell after latching on to a superb pass from Stewart Devine.
Referee Alan Freeland pointed to the spot and Chris Aitken drove the kick low into the left-hand corner, although the view of both managers after the match was that it was a soft award.
That may have been the case, but the hosts were worthy of their lead at that point, having played some neat passing football in the first half without the reward they deserved.
Defender Andy Graham twice came close to beating former Stirling keeper Mark McGeown but was just too high on both occasions, while at the other end Jerome Vareille passed up a great chance after 27 minutes – shooting weakly at Myles Hogarth.
Ayr only really woke up after going behind and skipper Ray Logan forced a couple of fine saves from Hogarth, but Stirling defended well and had the odd chance on the break – with Steven Bell having a good penalty appeal turned down and Dougie Wilson firing just over.