Patrick Asselin gave the hosts the lead after just 40 seconds before Joey Martin doubled the lead with a powerplay goal seven minutes later.
The Giants hit back through Cole Jarrett four minutes from the end of the period, but Andrew Hotham’s goal two and a half minutes in to the second period restored the two goal cushion.
British forward Matt Towe then pulled one back for the Giants before captain Blair Riley found an equaliser in the 37th minute.
With the game finely poised entering the final period, Steve Saviano added a third powerplay goal of the game for the Giants to put the Northern Irish side ahead for the first time.
In-form forward Sebastien Sylvestre put the game beyond doubt in the 55th minute, assisted by Saviano.