Dougie Freedman’s side had not lost in 13 previous games in the Sky Bet Championship - a run built on the back of their steely defensive resolve - but found themselves on the back foot when skipper Matt Mills’ own goal gave the visitors a 14th-minute lead.
And their first loss since November was sealed when 19-year-old Billing netted his first professional goal in spectacular fashion with a long-range 84th-minute strike as Huddersfield continued their steady improvement under David Wagner.
Forest had not conceded a goal in four previous league outings and it was particularly cruel that the run was ended by an integral member of the back four that had previously been so resolute.
Tommy Smith drove a low ball across the face of the Forest goal and Mills, looking to clear the danger, succeeded only in prodding the ball beyond goalkeeper Dorus de Vries.
Prior to that, Forest’s best chance had come when Ben Osborn had intelligently picked out Jamie Ward in the box, but he saw his shot charged down.
They responded to the Huddersfield goal with a dipping, swerving volley from the edge of the box from Nelson Oliveira, which missed the target by no more than a foot.
Robert Tesche went close with a header and Oliveira bent a lovely effort just wide of the upright from 18 yards.
But Huddersfield offered a reminder of their threat as Karim Matmour stung De Vries’ palms with a powerful shot.
Forest made a double change in just the 57th minute as they looked to find a way back into the game, with Oliver Burke and Jorge Grant introduced.
Grant was involved in the build-up as Oliveira went close yet again, this time with a thunderous low drive that Town goalkeeper Jed Steer somehow deflected around the post when it seemed destined for the net.
Steer then showed a fine turn of pace off his line to collect bravely at the feet of Eric Lichaj when it seemed the Forest full-back might just win the race to collect Vaughan’s incisive pass.
Forest wanted a penalty when Osborn’s crisp shot was blocked by Mark Hudson but referee Darren Deadman was unmoved.
And Huddersfield made certain of the three points when midfielder Billing conjured up a contender for the Terriers’ goal of the season with a simply stunning strike, sent arrowing into the top corner from 30 yards six minutes from time.
“It was a fantastic game and we did a lot of things right,” said Town chief David Wagner.
“I am very happy with the performance from my team because we spoke a lot last week about what we needed to do, particularly defensively. We wanted to keep a clean sheet or, at worse, concede only one goal.
“We know we are always able to score goals, we are dangerous as an attacking side and we knew we would have a chance if we could keep a clean sheet. But it is one thing to speak about this and it is another entirely to do out there and do it.
“In the second half in particular, this was one of the best performances we have seen since I have been here. All around, we deserved the win and it was a good day for us.
“In the first half we tried to create chances and we did that, it was an own goal but the moment that created the goal was very good.
“In the second half, we did not have to dictate the game, we only had to defend and use our speed to counter-attack. We beat Nottingham Forest with their own weapon, because that is what they like to do.”
Nottm Forest: De Vries, Lichaj, Mills, Mancienne, Jokic, Tesche, Gardner, Vaughan, Ward, Oliveira, Osborn. Subs: Cohen, Blackstock, Hobbs, Evtimov, O’Grady, Burke, Grant.
Huddersfield: Steer, Smith, Hudson, Lynch, Husband, Billing, Hogg, Bunn, Matmour, Lolley, Wells. Subs: Davidson, Whitehead, Murphy, Cranie, Dempsey, Manu, Bajaj.
Referee: Darren Deadman (Cambridgeshire)