A first-half Matt Mills own goal and a Phillip Billing screamer after the break handed the visitors victory on an afternoon when Forest struggled to create clear-cut chances.
Dougie Freedman named an unchanged team following last weekend's 1-0 win at Leeds. That meant that a defence of Eric Lichaj, Mills, Michael Mancienne and Bojan Jokic had the opportunity to continue The Reds' defensive solidity, while Nelson Oliveira was given a chance to build on his winning goal at Elland Road.
While it was Huddersfield who made the better start, Forest were the first team to test the opposition keeper. Mills peeled into space to meet David Vaughan's 13th-minute corner but he had a lot to do with his header, sending it straight at Terriers keeper Jed Steer.
Mills did have the ball in the net a minute later but, unfortunately for him and his team-mates, it was to the visitors' advantage. Tommy Smith's low cross from the right forced Mills into action and, positioned centrally six yards out, his attempted interception diverted the ball beyond Dorus de Vries and into the net.
It was proving to be a busy start for Mills, who conceded a free-kick in a dangerous area on 21 minutes when he brought down James Husband. Nahki Wells took responsibility for the set piece but he could only send the ball straight into de Vries' clutches.
Forest then came close to a spectacular equaliser courtesy of Oliveira. He received the ball from a throw-in down the right, allowing the ball to bounce and twisting his body to present himself with a shooting opportunity on his left foot. He sent the ball dipping just over the angle of bar and post.
The Reds' pursuit of an equaliser continued when another Vaughan corner caused problems for the Huddersfield defence. This time Robert Tesche was the beneficiary, out-jumping his marker to nod the ball just wide.
With half-time approaching, Oliveira had a good opportunity after receiving an excellent Ben Osborn cut-back. He collected the ball in time and space on the edge of the area and curled it agonisingly wide of the far post.
Huddersfield still looked a threat, however, and they could have made it 2-0 after a forward foray involving Wells and Harry Bunn. The ball was shifted to Karim Matmour on the edge of the area, who struck it into the ground to present de Vries with an awkward save. The Dutchman managed to push the ball to safety.
Two minutes were added at the end of the half, in the first of which Jokic worked himself a shooting chance on his right foot after a strong run forward and some neat footwork in the area. The Slovenian could only curl the ball high and wide, however.
And it was the Terriers who claimed the final shot of the half, Wells' low, powerful strike from 22 yards being comfortably held by de Vries.
There were no changes for either side at the break and Huddersfield had the first chance of the second half when Vaughan tripped Bunn on the edge of the box. Former Red Joel Lynch opted for power and saw his low strike diverted wide by the wall.
Freedman made a double change shortly afterwards, sending on youngsters Oliver Burke and Jorge Grant for Jamie Ward and Gary Gardner.
Shortly after his introduction, Grant made a good forward run. When the ball ran away from him Oliveira pounced, firing a powerful effort low towards goal. Steer managed to wildly push the ball behind.
Long-range left-footers from Oliveira, over the bar, and Tesche, straight at Steer, followed as Forest upped the ante in the search of a goal.
The game then entered a scrappy spell, with Forest's Grant and Huddersfield's Jonathan Hogg and Smith entering the book.
Town were proving themselves a tough nut to crack and Freedman decided to send on Dexter Blackstock with nine minutes to play, Tesche making way.
But the visitors wrapped the game up in stunning fashion seven minutes from time when Billing picked the ball up in space 30 yards out and struck the ball into the top corner.
It could have been 3-0 shortly afterwards when Jokic conceded possession to Matmour 20 yards out. De Vries had to get down low to make the save at his left post.
Five minutes of added time were indicated at the end of the match but there was nothing Forest could do to stop their long unbeaten run from coming to an end.
Forest: De Vries, Lichaj, Mills (c), Mancienne, Jokic, Vaughan, Gardner (Grant 57'), Tesche (Blackstock 81'), Ward (O.Burke 57'), Osborn, Oliveira
Subs not used: Evtimov, Cohen, Hobbs, O'Grady
Bookings: Grant 69', Mills 82'
: Steer, Smith, Lynch, Hudson (c), Huddersfield
Husband, Hogg (Cranie 90'), Billing (Whitehead 88'), Matmour, Bunn (Dempsey 90'), Lolley, Wells
Subs not used: Murphy, Davidson, Manu, Bojaj
Goals: Mills (o.g. 14'), Billing 84'
Bookings: Hogg 72', Smith 73'
Referee: Darren Deadman
Attendance: 19,984 (1,193 away)