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Ahmed El Mohamady came close shortly afterwards when the ball broke to him, but the Egyptian midfielder sent his shot whistling just past the post.
The breakthrough finally came just one minute after the restart when George Boyd latched onto Simpson's pass before sliding the ball past Smithies.
Vaughan then came close to getting a spectacular equaliser when he met Oscar Gobern's header with a bicycle kick, but his acrobatic effort went just wide.
Hull should have doubled their lead with just over 20 minutes remaining when Boyd was left free in the area. The striker swung his left boot at the ball, but fired his shot straight at Smithies.
Huddersfield pushed for an equaliser late on but couldn't breach the Hull defence and were forced to settle for a narrow defeat.body check tags ::