Hunt jinked past two defenders and blasted a low shot into the bottom left corner to stretch Town's unbeaten record to 20 matches.
Town were staring at a first defeat since Christmas when Posh midfielder Grant McCann scored a penalty on 41 minutes after Lee Peltier felled Craig Mackial-Smith in the box.
Gary Roberts should have levelled from the spot on 84 minutes when Hunt was brought down in the area but Peterborough keeper Joe Lewis made a brilliant save.
Peterborough should have been leading by more and were denied an early lead by Ian Bennett's brilliant save from George Boyd.
Bennett also saved from Charlie Lee while James Wesoloski hit the side-netting.