It was Stranraer's first league win since September, but although the home side began brightly enough, there was no hint in the first half of the mayhem which would erupt after the break.
Billy Reid's Accies went in at the break with a single goal lead after Brian Carrigan fired home a 39th minute free-kick from 25 yards.
But Ian Ross' leveller for Stranraer, which came four minutes after the break, kicked off a 32nd minute spell in which an incredible eight goals were scored.
Two minutes after that, Brown Ferguson's shot took a wicked deflection off a home defender to restore the visitors lead.
But Stranraer striker Michael Moore found the net twice in three minutes, both times with headers to put the home side ahead for the first time.
Back came Hamilton and back came Ferguson who levelled for Accies with a shot which dipped beyond Barry-John Corr in the 63rd minute.
Four minutes later Moore bagged the match ball with a clinical headed finish from Lee Sharp's corner.
But Graeme Jones had the visitors level yet again when he steered Scott McKenzie's cross beyond Corr with 20 minutes still remaining.
The only surprise of the closing stages was that only one further goal was scored.
It came for Stranraer with 11 minutes left when Shields - lurking at the back post - met Leigh Hinds' cross and headed decisively past David McEwan for the winner.