Michael McGowan's sumptuous opener in the 51st minute appeared to have secured the home side the three points.
But with seconds remaining defender Blair Spittal squeezed home an equaliser to salvage a point for Queen's Park, only their second of a miserable campaign so far which still leaves them nine points adrift of second-bottom Albion Rovers, who also secured a point in their match against high-flying Elgin City.
The Morayshire club passed up an opportunity to narrow the gap on the league leaders as they toiled to a forgettable 0-0 draw with the side from Coatbridge at Cliftonhill.
Indeed, the visitors had goalkeeper Raymond Jellema to thank for keeping them on level terms as he made important saves from Kevin Nicoll and Darren Miller.
Craig Gunn missed a late chance to snatch a scarcely deserved winner for Elgin, who remain in second position but are only two points from ninth place, with all the teams in the division bar Queen's Park separated by five points.
Stirling Albion picked up a valuable 3-1 victory over Montrose at Forthbank to move into third place in the table, with a single-goal difference separating them from the side above.
The home side started the match superbly and took a second-minute lead through defender Chris Smith's header, only for striker Bryan Deasley to quickly restored parity for the visitors with his slick turn and shot.
Jordan White pounced from close range to fire Stirling back in front shortly after half-time and the hosts made certain of victory when Sandy Cunningham raced clear to slot home their third in the 78th minute.
Clyde leapfrogged their hosts in the table after they emerged 1-0 victors over Berwick Rangers from an ill-tempered clash at Shielfield Park.
After a dreary opening period, Clyde scored what proved to be the winner in the 48th minute when Ryan Frances placed a clever looping header beyond Berwick's Paul Grant.
Clyde then had Iain Gray sent off for an overzealous tackle on Darren Lavery, but Berwick could not make their numerical advantage count.