The Terriers took a fifth-minute lead through Elias Kachunga's header but Jonny Howson equalised for the hosts just 66 seconds later.
Kachunga put the visitors back in front before the break when he poked an effort past John Ruddy via a deflection off Sebastien Bassong.
The Canaries had chances in the second half but defeat means they have now lost seven of their last nine games.
Relive Norwich v Huddersfield
For David Wagner's side victory was their third in successive games after five without a win, but their first goal came about in controversial circumstances.
Kachunga looked to be in an offside position when Tommy Smith crossed in from the right, however the header was allowed to stand.
The Canaries got back into the match almost immediately when Robbie Brady hooked a cross to captain Howson to head home his fourth goal of the season.
But, soon after Terriers forward Nahki Wells nearly capitalised on a wayward Graham Dorrans backpass, Kachunga was given too much space in the middle of the park to run forward, play a one-two with Smith and prod in his ninth of the campaign.
Kachunga missed a similar chance for a hat-trick in a second half which Norwich shaded, but could not find a way past Town goalkeeper Danny Ward, as Nelson Oliveira's attempted lob went wide of the mark when he was free in the box.
Sebastien Bassong almost equalised late on with a powerful header from a corner but it was not to be and the home fans let out a chorus of boos at the final whistle.
Norwich manager Alex Neil: "The disappointing thing is we had a lot of clear-cut chances that we didn't take.
"Ultimately goals change games. There was certainly enough there to score goals.
"In the first half we lacked intensity, we looked leggy. In the second half we were more energetic."
Huddersfield boss David Wagner told BBC Radio Leeds:
"We wanted to be confident and play with our identity. We were very strong in the first half and I think we deserved the three points.
"When you play Norwich away there will be hard moments but we were lucky and I'm very proud.
"Kasey Palmer was outstanding tonight. His work with and without the ball was class.
"This was a great week and I'm giving the players tomorrow off! It's important they spend time with their families around Christmas."
Match ends, Norwich City 1, Huddersfield Town 2.
Second Half ends, Norwich City 1, Huddersfield Town 2.
Substitution, Huddersfield Town. Michael Hefele replaces Rajiv van La Parra.
Attempt missed. Sebastien Bassong (Norwich City) header from the centre of the box is close, but misses to the left. Assisted by Robbie Brady with a cross following a corner.
Corner,  Norwich City. Conceded by Christopher Schindler.
Offside, Huddersfield Town. Tommy Smith tries a through ball, but Kasey Palmer is caught offside.
Attempt saved. Sebastien Bassong (Norwich City) header from the centre of the box is saved in the centre of the goal. Assisted by Robbie Brady with a cross.
Corner,  Norwich City. Conceded by Chris Löwe.
Aaron Mooy (Huddersfield Town) is shown the yellow card for a bad foul.
Foul by Aaron Mooy (Huddersfield Town).
Steven Naismith (Norwich City) wins a free kick in the defensive half.
Elias Kachunga (Huddersfield Town) wins a free kick in the attacking half.
Foul by Alexander Tettey (Norwich City).
Corner,  Norwich City. Conceded by Chris Löwe.
Substitution, Huddersfield Town. Philip Billing replaces Jonathan Hogg.
Attempt saved. Jacob Murphy (Norwich City) left footed shot from outside the box is saved in the bottom left corner. Assisted by Jonny Howson.
Attempt saved. Steven Naismith (Norwich City) right footed shot from the right side of the six yard box is saved in the bottom left corner. Assisted by Cameron Jerome with a headed pass.
Attempt missed. Robbie Brady (Norwich City) left footed shot from outside the box misses to the left.
Substitution, Huddersfield Town. Harry Bunn replaces Nahki Wells.
Offside, Huddersfield Town. Aaron Mooy tries a through ball, but Rajiv van La Parra is caught offside.
Kasey Palmer (Huddersfield Town) wins a free kick on the right wing.
Foul by Sebastien Bassong (Norwich City).
Attempt blocked. Robbie Brady (Norwich City) left footed shot from outside the box is blocked. Assisted by Jonny Howson with a headed pass.
Nahki Wells (Huddersfield Town) is shown the yellow card.
Offside, Huddersfield Town. Rajiv van La Parra tries a through ball, but Nahki Wells is caught offside.
Foul by Elias Kachunga (Huddersfield Town).
Robbie Brady (Norwich City) wins a free kick on the left wing.
Jonathan Hogg (Huddersfield Town) wins a free kick on the right wing.
Foul by Robbie Brady (Norwich City).
Attempt missed. Nahki Wells (Huddersfield Town) left footed shot from the left side of the box is close, but misses to the left. Assisted by Aaron Mooy.
Kasey Palmer (Huddersfield Town) wins a free kick on the left wing.
Foul by Jacob Murphy (Norwich City).
Hand ball by Alexander Tettey (Norwich City).
Attempt missed. Jacob Murphy (Norwich City) right footed shot from outside the box is close, but misses to the right. Assisted by Cameron Jerome.
Substitution, Norwich City. Cameron Jerome replaces Nélson Oliveira.
Substitution, Norwich City. Steven Naismith replaces Graham Dorrans.
Attempt missed. Nélson Oliveira (Norwich City) right footed shot from outside the box is high and wide to the right.
Attempt missed. Aaron Mooy (Huddersfield Town) left footed shot from outside the box misses to the left.
Kasey Palmer (Huddersfield Town) wins a free kick in the attacking half.
Foul by Sebastien Bassong (Norwich City).
Huddersfield moved up to third in the Championship with victory at Norwich.