Teenage striker Andrew Ferguson kept Ayr's slim promotion hopes alive with the winning goal in this tight match.
Both sides had chances in a game that could have gone either way, but Ferguson's late winner was enough for Ayr.
A quiet first half ended with Ayr taking the lead when Craig Conway crossed for Paddy Connolly to stab home from close range.
Morton replied within two minutes of the re-start when Paul Walker charged through to fire home from 18 yards.
Morton enjoyed their best spell after that with Chris Templeman and Jason Walker both going close to putting them in front.
But Ayr slowly battled back and struck their winner in the 76th minute when a Conway corner was flicked on by Gareth Wardlaw and Ferguson turned to fire home from six yards.
Ayr could have added further goals, and Willy Lyle fired just wide in the closing minutes.