Billy Sharp's early goal was enough to seal victory for the Iron at Saltergate, and although the home side had large amounts of pressure United keeper Joe Murphy was rarely tested.
Laws said: "We came here when they were on a real roll, and we knew it was going to be a tough game.
"We had to dig in and it was an awful night for football with the wind blowing from goal to goal but we were solid and worked really hard and this was all about the work ethic.
"Billy is sharp in name and sharp as a player. He's got the ability to sniff out opportunities and he thought the keeper might spill the ball. It was a typical goal from him."
Chesterfield had won their last two home games, including a 2-1 Carling Cup success over Premiership side Manchester City.
Spireites manager Roy McFarland said: "They say football can be a seven day wonder.
"We'd won our previous two home games but this game can put you very firmly on your backside when you least expect it.
"They defended very well and did a job on us but we didn't move the ball around and we didn't attack one or two very good crosses we put in.
"We didn't really click. It was a scruffy game with few chances for both teams, but they took their chance."