It was the Wolves who took the lead in the opening minutes following a slick passing move, which allowed Monaghan to cross the line for a try.
The Giants hit back to level the scores soon after when Danny Brough made the most of an industrial yet effective move to score a scrappy try between the sticks.
Huddersfield then edged ahead after Jake Connor's try was approved following a video decision taking the score to 10-6, but Brough missed the kick that would have put the Giants two points further in front.
However, the Wolves took a lead into half time following good work from Monaghan and Grix who produced tries, leaving the scores at 18-10 at the break.
The Wolves went further ahead soon after the interval when Atkins collected well to score, though their lead was cut down when Jermaine McGillvary hit back for the Giants, with the conversion taking the score to 24-16 to the home side.
The Giants looked like they were going to mount a revival of sorts as Dale Ferguson broke through the Wolves defence with a great run, which then allowed Brough to kick his side within two points of the leaders.
The Wolves proved too much in the final stages of the game as Grix grabbed his second try of the night, leaving Stefan Ratchford to kick Warrington to a 30-22 victory.