Hull KR: (8) 16
Tries: Bauer, Gene
Goals: Cooke 4
Huddersfield: (12) 28
Tries: Jones, Raleigh, Wild, Lolesi
Goals: Thorman 6
Paul Cooke's debut for Hull KR ended in disappointment as Huddersfield put in a strong second-half display to claim their fifth straight win.
After trailing 12-0 early on, Hull KR turned it around with tries from Andreas Bauer and Stanley Gene and four Cooke goals to lead 16-12.
But the Giants dug deep and Stephen Wild and Jamahl Lolesi edged them ahead once more in the final quarter.
Chris Thorman kicked six goals to help the Giants to another success.
Hull KR coach Justin Morgan
"I thought he (Cooke) was great. He kicked well and I said before the game that he wouldn't have a problem settling in and I think that we saw that.
"He kicked the ball exceptionally well, defended well and gave us good direction. The players are only going to get better when they get used to playing with him.
"We've got a week's worth of training to get some understanding and I expect an improved performance from everyone next week."
Huddersfield coach Jon Sharp
"In our previous games we've seen a side that dominated field position, but this was a different type of performance.
"We had to defend resolutely, show a focus and a commitment to the gameplan. We showed a patience and that comes from the first seven weeks of disappointment.
"That galvanised us and brought us together, which showed tonight."
Hull K R: Cockayne, Hardman, Dyer, Goddard, Bauer, Cooke, Webster, Aizue, Fisher, Vella, Chester, O'Neill, Gene.
Replacements: Ward, Gannon, J. Netherton, Lennon.
Huddersfield: Thorman, Reilly, Lolesi, Wild, Aspinwall, Drew, Brown, Mason, Hudson, Skandalis, Nero, Raleigh, Jones.
Replacements: Crabtree, Jackson, Griffin, Snitch.
Referee: P Bentham (Warrington)