David Wagner's side, meanwhile, remain without a win in the league this term and boast just one victory from their last 15 games.
The hosts began brightly at the John Smith's Stadium as Philip Billing's throw-in was flicked on to Elias Kachunga in front of goal after just two minutes, but the offside flag put an end to the move.
Huddersfield would attempt to use Billing's throw-in to their advantage in a bid to make headway inside the Eagles box early on in the encounter, but the visitors were alert and able to repel each foray into their area.
The first concrete chance of the game did not arrive until the 18th minute, when Chris Lowe's pinpoint delivery into the Palace box was met by Steve Mounie, only for the 23-year-old's header to sail just over the bar.
However, the Ivorian winger was responsible for a moment of magic to break the deadlock, embarking on a jinking run from the far side, knocking the ball past two defenders and rifling the ball past Jonas Lossl.
Huddersfield responded well to falling behind, with Billing's goal after the restart disallowed due to an earlier foul, while Aaron Mooy unfortunate not to level when his 59th-minute strike hit the woodwork with Wayne Hennessey beaten.
Meanwhile, a second for Palace was ruled out for a foul by McArthur on Lossl, with Zaha a constant thorn in the opposition's side, and in the end the Eagles were able to hold on despite Huddersfield launching a late blitz against their opponents.
HUDDERSFIELD TOWN (5-4-1): Lossl; Hadergjonaj, Zanka (Depoitre 78'), Schindler, Kongolo, Lowe; Billing, Van La Parra (Mbenza 78'), Mooy, Kachunga (Diakhaby 68'); Mounie
CRYSTAL PALACE (4-3-3): Hennessey; Wan-Bissaka, Tomkins, Sakho, Van Aanholt; Milivojevic, Kouyate, McArthur; Townsend (Schlupp 90'), Ayew, Zaha