County got away with a blatant truck and trailer move off a maul and Andrew Goudie found a huge gap to go through for a try which he converted in four minutes.
Hawks levelled five minutes later, Gary Adams picking up at the back of an advancing scrum five, before dummying and charging over, with Liam Brims converting.
As conditions worsened, the handling deteriorated, but penalties from Goudie and Jonny Hope enabled the visitors to turn round leading 13-7.
Stirling took advantage of a yellow card for Fraser Hastie and another refereeing error for George Arnott to score and Goudie convert. Back came Hawks and James Couper did well to chase and touch down a Brims kick through to make it 12-20.
Late tries from Ali Mackie and Scott Derrick, however, gave County the win and the bonus point from an error-strewn but entertaining game in poor conditions.