Jordan Rhodes fired wide from an early opportunity for the visitors before Vale's Marc Richards squandered his team's best chance of the match in the 10th minute. Poor defending by Huddersfield enabled Kris Taylor's cross to drop straight at Richards' feet, but the striker dragged his shot horribly wide from close range.
The visitors made them pay just two minutes later when centre-back Clarke netted the winner with an overhead kick from 12 yards.
Vale's defence struggled to clear after Peter Clarke nodded Robbie Williams' free-kick into the danger area and Nathan Clarke's spectacular strike kissed the underside of the bar on its way in.
Huddersfield settled to play some excellent football after that and dogged Vale did well to avoid further damage before the interval.
The second half was much more even with Vale attempting to force the pace, but the quality of the game deteriorated and neither side created a chance of note.