It looked like the Giants had snatched the two points when Chris Thorman slotted over a one pointer in the 75th minute, but Horne kept his cool to ensure a reward for his side's efforts.
Thorman had given the Giants the lead after a quarter of an hour, and his converted try was the only score in a tight first half, the Giants going in 6-0 to the good.
Danny Tickle got Hull back on level terms with a converted try on his own, before the duo exchanged penalties to level things up at 8-8.
Hull dominated field position and possession for much of the game, but as has been the case for most of the season, the Giants defence held firm.
Then just as it looked like Thorman had snatched the victory for the visitors, Horne popped up to finish the game 9-9.