With leaders Serbia facing Wales in a later kick-off on Sunday, Martin O'Neill's side needed just a point to - temporarily at least - move top of what is proving to be a tightly contested group.
And, despite a flat first-half performance, a late glut of pressure from the hosts resulted in Walters thumping home a deserved equaliser to cancel out Martin Hinteregger's opener.
Shane Duffy thought he had snatched a winner two minutes later, only for the referee to disallow the header for a foul by the defender, who led with a raised arm.
