The Giants, who won at Wigan 12 months ago, pulled off another stunning opening-round victory to give Brown's successor Paul Anderson a dream start to his first full season in charge.
Huddersfield's seven-try rout also marked a tremendous start for new captain Danny Brough, whose superb tactical kicking kept Saints pinned inside their own half for most of the first half to create the position for his side to outplay their hosts.
New forward signings Stuart Fielden and Craig Kopczak helped lay a solid platform for the visitors, while hooker Shaun Lunt made a try-scoring return from his loan spell at champions Leeds.
Jermaine McGillvary, Brett Ferres, Leroy Cudjoe (two), Luke George and Larne Patrick also crossed for the Giants, while Mark Flanagan scored Saints' only points of the game with a second-half try.
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- Danny Brough