Huddersfield produced a powerful second-half display to record a win which ensures Castleford remain rooted to the bottom of the table.
David Hodgson and Jamahl Lolesi put Huddersfield ahead, but Cas went into the break level at 14-14 after tries from Richard Owen and Luke Dorn.
The Tigers' hopes suffered a major blow when replacement Michael Korkidas was sin-binned just after coming on.
And the Giants capitalised with four second-half scores sealing the victory.
Two tries in three minutes had put the visitors in charge early on.
Stephen Wild and Paul Whatuira worked the move to put winger David Hodgson in at the corner for the 100th try of his career while back rower Lolesi scored the Giants' second try after Luke Robinson and Kevin Brown provided the opening.
Castleford, who had taken the lead with a Craig Huby penalty, hit back on 22 minutes when teenage winger Richard Owen scooped up a pass to touch down in the corner.
A Thorman penalty gave Huddersfield a six-point advantage but it was all square at the break as Tigers half-back Dorn pounced on a kick from Brent Sherwin to claim his 16th try of the season.
606: DEBATE
Less than a minute after taking the field, Korkidas was sin-binned for a reckless challenge on Robinson - an offence which enabled Thorman to stretch the lead to 20-14.
A minute later, prop Darrel Griffin and Tigers half-back Ryan McGoldrick were yellow-carded for fighting.
Another Thorman penalty nudged the Giants further ahead before a late points flurry - Whatuira scoring following a 90-metre break by full-back Leroy Cudjoe, Griffin charging over from close range, and a final-minute Thorman try - completed the resounding victory.
Castleford coach Terry Matterson:
"The scoreline was harsh but we played some good football. It was a great contest for 60 minutes until one silly thing from one of my players. It was a big turning point.
"Our effort and endeavour was really good for the first hour but I was really disappointed with the last eight minutes of the match."
Huddersfield caretaker coach Paul Anderson:
"Top six is our goal. Until someone says there is no way we can make the play-offs, we will always believe it is still possible.
"We are looking up. We have pulled away from the bottom two and now my concern is to catch the teams in front of us."
Castleford: Donlan, Owen, Shenton, Lupton, Wainwright, Dorn, Sherwin, Higgins, Henderson, Huby, Guttenbeil, Westerman, McGoldrick.
Replacements: Korkidas, Boyle, Sargent, Arundel.
Huddersfield: Cudjoe, Aspinwall, K. Brown, Whaturia, Hodgson, Thorman, Robinson, Mason, Hudson, Griffin, Wild, Lolesi, Raleigh.
Replacements: Crabtree, Jones, Jackson, Kirmond.
Referee: R Silverwood (Dewsbury).
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