Forest Green started the stronger of the two sides, with defender Luke Oliver twice directing headers wide of the post as Halifax struggled to get going at The New Lawn.
Their pressure paid off after 20 minutes as they finally took the lead. Sam Wedgbury whipped in a cross from a wide position and Norwood was on hand to head home at the back post.
Rovers continued to impress, with Norwood having a chance deflected straight at the goalkeeper, but they doubled their advantage just before the half-hour mark when Clovis Kamdjo burst clear of the defence before crossing for Parkin to convert from close range.
Halifax improved before the half-time whistle, with Matty Pearson seeing a shot deflected at the goalkeeper, but the Shaymen couldn't break through and they have it all to do in the second half.