Michael Moffat, who declared the Pars could still finish in the top four prior to this fixture, put his money where his mouth was by netting his first goal since 10 December.
However, the excellent Joe Thomson secured a point for Gary Naysmith’s men, clinically finding the net for the fourth time in eight outings since arriving at Queens on loan from Celtic.
The Pars will look back ruefully on Nicky Clark’s late effort, the former Rangers striker – who notched a quadruple against Dumbarton on Saturday – seeing a wonderful shot from the edge of the box rattle the post.
Morton, occupying fourth spot, now have a seven-point lead over Queens, with the Pars a further four back. It looks a tall order for either to catch the Ton.
It took just 17 minutes for Moffat to give the hosts the lead, the former Ayr favourite scampering on to a hopeful lofted through ball and nudging the woefully weak Darren Brownlie off the ball before slotting beyond Lee Robinson.
However, Queens have been admirably resolute since the arrival of Naysmith – their disappointing defeat by Falkirk on Saturday aside – and their response was swift and effective.
John Rankin benefited from another mishit as his trundling drive from the edge of the box skewed into the path of Thomson, who controlled the ball instantly and fired beyond Sean Murdoch.
While breaking into the Celtic side appears an onerous task for any young Scot at the moment, Thomson increasingly looks the real deal – and he almost gave Queens the lead on the stroke of half-time, latching on to a neat Stephen Dobbie pass before fizzing a low shot just wide.
Dobbie was then denied by Murdoch following a mazy run and shot.
However, the best chance for either side to claim a precious win came and went when Nicky Clark found himself on the end of a sweeping Pars counter-attack, only for his curling drive from 18 yards to strike the inside of the post.
There was still time for John Herron’s point-blank header to force a superb save from Lee Robinson.