Shildon lost for the first time since early October despite taking a 2-0 lead into half time.
Billy Greulich-Smith gave Shildon the advantage at half time with 2 well taken goals.
In the second half Consett, Danny Craggs scored twice from set pieces. The first a well taken free-kick from 20 yards and the second from the penalty spot. In the closing minutes Jordan Nellis scored to take all 3 points.
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