Huddersfield (12) 25
Tries: Jensen 2, Jackson, Thorman Goals: Thorman 4 Drop Goals: Thorman
Bradford (16) 24
Tries: Platt, Newton, Lynch, Finnigan Goals: Harris 4
Huddersfield captain Chris Thorman kicked an injury-time drop goal to earn his side a thrilling win.
Bradford's Iestyn Harris scored a 79th-minute penalty before Thorman popped up in an exciting finale.
Huddersfield trailed 22-12 after an hour but fought back in impressive style with Rod Jensen, who scored two tries, at the heart of their good play.
Welshman Harris scored four goals and Michael Platt, Terry Newton, Andy Lynch and Simon Finnigan went over for tries.
There was controversy when the hooter sounded as Bradford were preparing for a scrum and Bulls centre Paul Sykes was shown a red card for protesting to referee Steve Ganson.
Ganson had earlier sent four players to the sin bin - Leroy Cudjoe and Ryan Hudson of Huddersfield and James Evans and Ben Jeffries. The referee also placed three Bradford men on report.
Huddersfield's acting boss Paul Anderson:
"We played for 80 minutes, dug in and got our rewards at the end.
"We played for 17 minutes with 11 men and only conceded one try in that time so you have got to give credit to the Huddersfield guys.
The coach added: "I thought we defended really well."
Bradford coach Steve McNamara:
"I thought it was a pantomime out there.
"We are here talking about officials' performances and the effect they have on results."
Huddersfield: Cudjoe, Jensen, Lawrence, Whaturia, Elford, K. Brown, Thorman, Mason, Mason, Jones, Jones, Raleigh, Raleigh, Wild, Lolesi, Snitch, Griffin, Jackson, Kirmond, Hudson.
Sin Bin: Cudjoe (21), Hudson (27).
Bradford: Platt, Evans, Sykes, Nero, Tadulala, Harris,Jeffries, Vagana, Vagana, Newton, Lynch, Lynch, Solomona, Langley, Burgess, Godwin, Finnigan, Feather.
Sin Bin: Evans (43), Jeffries (54).
Ref: S Ganson (St Helens).