A first-half Francis Jeffers strike proved decisive, despite a nervy final few minutes at Hillsborough.
Laws said afterwards: "I'm emotionally drained and gave my players a right rollicking after the game for putting me through this agony.
"It's a great relief and it's been a long time coming. We needed bravery out there and a bit of calm and this had all the ingredients.
"There's been a millstone around our necks which has been getting heavier, but that showed morale in the camp is still there.
"There's no way on God's earth we will turn around and think we are okay, we are not.
"It's the worst record in the history of the club and who wants to be associated with that? But that will go a long way to building confidence."