Hastings had looked to be on their way to a third successive league win until a last-minute freak equaliser.
Geoff Neville's third minute goal put Burnham 1-0 up but Carl Rook equalised six minutes before half time.
Hastings took the lead on 70 minutes after Steve Hafner blasted home a free kick from the edge of the box as Burnham organised their wall.
But in the 90th minute substitute Jon Horsted unleashed a left wing cross which deceived everyone and flew over keeper Will Toal into the top far corner of the net to earn the visitors a draw.
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