Layne Ulmer and Gleason Fournier put the Devils 2-0 in front, before Colin Shields halved the deficit late in the first period.
Guillaume Doucet made it 3-1 midway through the second session, but Chris Higgins quickly hit back to keep the Devils in the game.
Joey Martin scored on a breakaway to restore the Devils’ two goal cushion just before the second buzzer.
The Giants refused to lie down and final period goals from Shields, Brandon Benedict and Jim Vandermeer secured the win to set up an intriguing second in Belfast next Wednesday.
(Image permission: Helen Brabon)