Luke Garrard’s side triumphed 2-1 in the first of the play-off Eliminators - and will now travel to Harrogate Town next weekend for the semi final.
They are one victory from another final after being edged out by Tranmere Rovers two years ago.
Pete Wild’s away side went ahead less than 20 minutes into the tie and that’s how it stayed until half-time.
Tobi Sho-Silva burst through the middle and got an all-important toe to the ball to prodded it past the goalkeeper.
But they didn’t count on an incredible second-half comeback.
Wood made it 1-1 when Kane Smith stuck eight minutes into the second-half.
Matt Rhead knows all about how to win promotion and when he nodded the hosts ahead with ten minutes to go in knocked the stuffing out of Halifax.
Winning manager Garrard, pictured, said: “I was very calm at half time and I’m thankful for that as they really went and delivered in the second half.
“I’m delighted for the boys, I’m over the moon. We’ve given them a few days off now so they can come back and really be ready for difficult semi-final.”