Scrum-half Luke Robinson scored twice in an eight-try demolition as Huddersfield won at home for the first time since July last year.
Robinson took advantage of a wind-assisted forward kick to power over for his first try just before half-time to leave the Giants 28-0 up after the break.
He then further increased Huddersfield's lead on 60 minutes when a pass from Brett Hodgson put him in the clear.
Huddersfield's victory was their first at the Galpharm Stadium since a 25-24 win over Bradford near the end of last season.
Quins made a strong start with David Howell twice going close from Danny Orr's well-placed passes only for the youngster to be held up on the line.
Orr then failed to hold a long Giants punt forward on seven minutes and Stephen Wild pounced on the mistake to give Huddersfield the lead under pressure from Quins skipper Rob Purdham.
The visitors seemed to lose confidence after that and went on to produce an error-strewn performance which gifted Huddersfield an easy victory.
A spell of pressure near the Quins try-line eventually saw Robinson collect a roll-back and he fed Keith Mason for an easy score on 19 minutes.
Quins winger Tony Clubb tried to intercept Robinson's pass to Leroy Cudjoe but only succeeded in diverting the ball to Kevin Brown for another easy try.
Quins' afternoon was summed up on 67 minutes when Brown stole the ball from Orr and romped home for a superb solo try under the posts.
Orr got some pride back by converting Danny Ward's consolation try nine minutes from time but Huddersfield youngster Shaun Lunt had the last word with a solo effort converted by Cudjoe.
Quins, managed by former Giants assistant coach Brian McDermott, had been gunning for a third straight win but looked a shadow of the side which scored 60 points against Warrington last week.