The hosts made a bright start to the match and went ahead in the 12th minute when Stuart McColm blasted in from 18 yards out.
McColm doubled his side's lead shortly after half time when he found the bottom corner of Neil Parry's net from the edge of the area.
The game was then turned on its head when three goals in eight minutes saw Queen's Park take the lead.
Less than a minute after McColm scored his second, Michael Keenan headed in from 12 yards out to make it 2-1.
Anthony McParland drew the Spiders level in the 58th minute when he thumped his 25-yard free kick into the top corner, before Lawrence Shankland completed the rout two minutes later, turning the ball in from six yards out to steal all three points.