Michael Rose looked to have sent them on the way to a fourth straight win only for substitute Connor Murray to equalise a minute after his introduction.
In an action-packed first half the overwhelming majority of chances fell to Ayr but the best effort came from Queens, with Stephen Dobbie rattling an angled 18-yard drive off the post.
Prior to that, Craig Moore twice went close for Ayr before Lawrence Shankland caused problems with a couple of free kicks.
Visiting goalkeeper Alan Martin made a superb save to keep out a rasping shot from Alan Forrest and six minutes into the second period Dobbie’s shot on the turn was well saved by Ross Doohan.
Rose broke the deadlock in 75 minutes when he headed home a Forrest corner but Queens won themselves a point when Murray drove home after a Callum Fordyce header.