A first half strike by James Tomkins and a Luka Milivojevic penalty were enough to see off a horribly below par home side.
Far too many in the Town ranks were off the pace, it being telling that 81 minutes had been played before Rajiv Van la Parra brought the first save of the afternoon from Wayne Hennessey.
Defeat means Roy Hodgson’s Eagles are now just a point behind the Yorkshire club heading into the international break.
Palace went ahead midway through the first half after Town had been unable to clear a corner from Luka Milivojevic.
The hosts had two stabs at goal inside the six yard area, James Tomkins putting the second of those in from close range.
Town clearly hadn’t learned their lesson, as just after the hour mark Tomkins was again left all alone at a corner only to this time stab his shot against the post.
Huddersfield’s best chance came soon after the let-off, as Steve Mounie fired narrowly wide from a cross by Florent Hadergjonaj.
Palace doubled their lead on 68 minutes, a dreadful attempt at a slide challenge by Mathias Jorgensen seeing Andros Townsend upended and Mike Dean left with no option but to point to the spot.
Milivojevic did the honours from the spot, sending Jonas Lossl the wrong way to clinch a win that, come the season’s end, could be very important.
The FA Cup quarter-finals taking place this weekend meant Swansea, West Ham and Southampton were all without a game in the league - handing a golden chance to either Town or Palace to boost their own survival hopes.
In the end, the Londoners were the ones to take advantage by avenging their opening day loss to David Wagner’s men.
Palace were full value for the win, too, to leave Town needing to find a response when the Premier League resumes after the international break with an Easter Saturday trip to Newcastle United.