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Blair Alston opened the scoring for the Bairns on the brink of half-time, heading an Aaron Muirhead cross into the bottom corner.
John Baird netted his 18th of the season shortly after the break.
But Derek Lyle pulled a goal back with a neat turn and finish and Iain Russell's strike levelled the scores in stoppage time.
Queen of the South fought back from two goals down to draw with promotion-chasing Falkirk in the Championship.