It was the home side that broke the deadlock through a Michael Platt try, but the Giants went into the break with a lead after Jermaine McGillvary and Luke George went over.
The visitors dominated play after the break, inspired by a superlative performance from Danny Brough. The half-back scored two penalties and a try as the Giants asserted their dominance.
Danny Addy added some consolatory points to Bradford's tally, capitalising on Joe Wardle's indiscipline with a penalty kick.
It was an ill-tempered second half, with Huddersfield second-row Luke O'Donnell sin-binned after a scuffle.
The result saw Huddersfield claim their fourth win on the bounce to keep the pressure on second-placed Wigan Warriors.