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Goals from Claus Jorgensen and Robbie Williams condemned Town to a first defeat in caretaker boss Gerry Murphy's six-match reign.
This looks certain to be Murphy's last game in charge, with former Barnsley manager Andy Ritchie set to be appointed ahead of Saturday's trip to Scunthorpe.
Blackpool, backed by 2,463 supporters, were at Huddersfield right from the start with Keigan Parker forcing Matt Glennon into an early tip-over.
From the resulting corner striker Andy Morrell just failed to connect with a point-blank overhead kick.
Hudson's flicker header from Jon Worthington's free-kick brought a superb reflex save from the wrong-footed Hart and he kept Huddersfield at bay throughout.
Jorgensen's goal came just before the half-hour and again Parker was the man to cause problems for the Huddersfield defence.
Parker collected the ball and fired at goal only for David Mirfin to hook off the line. The rebound fell perfectly for Jorgensen who steadied himself and finished hard and low into the bottom left corner.
Andy Booth headed straight at Hart early in the second half, but the Seasiders sealed it on the hour when Williams fired home after Glennon had blocked Ian Evatt's header.
Hart was the hero with two first-class saves to preserve the points. First he denied Beckett, who was put clear by Adnan Ahmed and then he flung himself to turn Sinclair's powerful header round the post in stoppage time.