The home side started brightly and were rewarded as Liam McAlinden diverted Jordan Clark's shot into the net.
David Ball had a great chance to level for the visitors before half-time but goalkeeper Mark Halstead denied him brilliantly.
With time running out Hunter expertly blasted past Halstead as the game ended in a draw.
Shrewsbury Town manager Micky Mellon told BBC Radio Shropshire:
"It was extremely difficult conditions for both teams to play any sort of attacking football - but on the balance of chances we'll be pleased with a point.
"It was a catalogue of errors from us in the lead up to the equaliser - and it's disappointing for us to concede so late on in the game.
"We wanted to see through the result as we move on to Monday, but the important thing is that we haven't lost the game today against our rivals."
Substitute Ashley Hunter's late strike helped Fleetwood earn a vital point against fellow strugglers Shrewsbury.