The Robins raced into a 16-0 lead in front of their 2,000-strong away support at the Galpharm Stadium but had to hold on in the face of a comeback from the home side to claim what was a shock win.
The Giants had looked like a team to be reckoned with in narrow defeats at the respective hands of St Helens and Bradford Bulls, but now sit bottom of the Super League table as the only side yet to pick up a point.
Huddersfield could not find a way back into the game at that stage, and Rovers extended their lead with three penalty goals from Gareth Morton before Ben Cockayne grabbed a second touch down.
At 16-0 down it could have been all over for the Giants, but Eorl Carbtree sent Stephen Wild over to give the home side some hope just a minute before the half-time interval.
Huddersfield dominated the early exchanges after the restart, and the pressure finally told when Chris Nero pounced on Chris Thorman’s kick into the in-goal area to score, reducing the arrears to 16-10.
Other than this the Rovers defence held firm, and James Webster potted a drop goal to wrap up the scoring and put the game just beyond the reach of the Giants.