Super League champions Bradford made it three wins out of three this season to end Huddersfield's unbeaten record.
Huddersfield (2) 6
Bradford (4) 20
Tries: Johnson 2, Deacon
Goals: Deacon 4
Huddersfield trailed 4-2 at half-time after Paul March had kicked one penalty and Bradford's Paul Deacon two.
Centre Paul Johnson scored the Bulls' first try, only for the home side to hit back when Darren Turner went over.
But the Giants had Hefin O'Hare sent to the sin-bin, and Deacon and Johnson added tries in the final 10 minutes to wrap up the win for the Bulls.
Huddersfield had conceded an average of 50 points in each of their last six meetings with Bradford, but for more than an hour they were in sight of a first-ever Super League win over them.
They had claims for a penalty try turned down on 36 minutes when Marcus St Hilaire was obstructed in pursuit of a kick to the corner, with Tevita Vaikona sent to the sin-bin.
Bradford were down to 11 men a minute later when Stuart Fielden was punished for the latest in a series of technical fouls at the play-the-ball.
Huddersfield hooker Sean Penkywicz was also shown a yellow card three minutes
into the second half, and the Bulls rode their luck to seal it late on.
Huddersfield coach Jon Sharp claimed the match was a moral victory.
"My team were the winners today," insisted Sharp. "I'm proud of them. I thought they did exceptionally well."
Bradford coach Brian Noble, meanwhile, was delighted with the way his side held their line intact while down to 11 men.
"We showed a lot of toughness," he said. "We had to roll our sleeves up and I thought our defence was magnificent but it had to be.
"Huddersfield are a good team and full credit to them. "
Huddersfield: Reilly, O'Hare, Nero, Bailey, St Hilaire, Gene, March, Slicker, Turner, Fleary, Jones, Roarty, Costin. Replacements: Donlan, Penkywicz, Smith, Crabtree.
Bradford: Reardon, Vaikona, Bridge, Johnson, Vainikolo,
L. Pryce, Deacon, Vagana, Smith, Fielden, Peacock, Parker, Radford. Replacements: Paul, K. Pryce, Langley, Anderson.
Referee: Russell Smith (Castleford).