Striker Alan Lee played after suspension and winger Danny Ward was a substitute after he recovered from a shin injury. Striker Jordan Rhodes was away on international duty with Scotland and both Jack Hunt and Liam Cooper were ineligible. Swindon were not allowed to play Liam Ridehalgh who is on loan from the Terriers.
Lee Novak opened the scoring for the Terriers after 22 minutes, following good work from Tommy Miller.
But Huddersfield were back on level terms on 36 minutes, Aden Flint equalising for the League Two club.
Raffaele De Vita (39) put Swindon in front before second-half goals from Mehdi Kerrouche and Simon Ferry wrapped up an FA Cup upset.
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