In wintry conditions, James Tomkins caught Town cold in the 23rd minute, prodding home from a corner to send the visitors into a deserved first-half lead.
And Eagles skipper Luka Milivojević sealed the victory with a second-half penalty after Andros Townsend was needlessly brought down in the area by Mathias 'Zanka' Jorgensen.
In truth, David Wagner's side were second-best for the majority of the encounter with it taking the Terriers until the 81st minute to register a first effort on target - a tame strike by Rajiv van La Parra.
The result leaves Town in 15th place in the Premier League table with Palace moving out of the drop zone, just behind the Terriers.
If you were at the John Smith's Stadium yesterday then you may have been snapped by our photographer – scroll through the gallery above to see.