In a bright start, Pools went close when Ritchie Jones crossed low from the right and the ball evaded the on-rushing Andy Monkhouse, while goalkeeper Alex Smithies stopped Denis Behan's effort.
But a 15th minute penalty put the Terriers ahead after defender Sam Collins and Scott Flinders got into a muddle and the goalkeeper felled Lee Novak, with Gary Roberts slotting the spot-kick home.
Adam Boyd's volley looked like levelling for the relegation-threatened home side, only for Antony Kay to spectacularly head off the line.
And the visitors made sure of the points two minutes later. Lee Novak met Anthony Pilkington's cross with his head and, after Collins was unable to clear and it bounced off the bar, Neal Trotman converted from close range.