Layton Maddison pounced first, ghosting onto a pinpoint through ball after 15 minutes before lashing home.
Jordan Nuttell doubled the Poachers' lead after 31 minutes with a well-crafted goal from a corner. It came short to Liam Adams, whose clever lofted cross was headed back across the keeper.
Hucknall had shown plenty of endeavour, boosted by their midweek win, and came closest in the first half when Travis Portas pushed a free-kick onto the post.
They did pull one back after 68 minutes when a shot deflected to Nathan Kelly who dispatched it past Travis Portas. The goal stood despite furious protests by Portas and Beeson that Kelly had been offside.
But Fraser Bayliss restored the home side's 2-goal cushion 7 minutes later.
Marshall Young saw his shot unluckily bounce off the post in the closing moments.