But Andreas Bauer's try on the 20 minute mark, together with Cooke's first points in the red and white, dragged the Robins back within 4.
And after the interval, Stanley Gene crossed for a try, converted by Cooke, before the stand off slotted over his fourth goal of the night to put Rovers 16-12 up.
Jamahl Lolesi sealed the win for the Giants with 7 minutes to go, with his converted try extending the lead to 26-16, before Thorman rounded off the scoring with another penalty.
Many regard the signing of Cooke as Hull KR's saviour, but it's games like this they have to win if they are to stay up. Huddersfield, meanwhile, continue their remarkable turnaround, as they move in to the top 6, with 5 straight wins propelling them up the table.