Carnell brought down former Aston Villa striker Stefan Moore when he was through on goal and referee Hooper sent the keeper off.
Midfielder James Ogoo was the man sacrificed by Curzon boss Gary Lowe with substitute goalkeeper Denis Barlow sent on.
But Harriers didn't take long to make their numerical advantage count, and it was the lively Moore who scored. Keith Lowe swung in a dangerous cross from the right and Moore bundled the ball in from close range.
Kidderminster's extra quality showed after the break and they doubled their lead when skipper Mark Creighton rose highest to head home Martin Brittain's corner.
UniBond North minnows Curzon struggled to make an impact on the game in front of their 277 visiting fans, with Alex Elliott having their best chance with a shot that flashed wide of the post early on.
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