The Iron dominated possession throughout, but had to wait until the 68th minute before midfielder Mark Duffy broke the deadlock.
“It was a good performance from us, but we knew we had to be patient to try and break Stevenage down,” Laws said.
“I told my players at half-time that the game was there for the taking for us if we wanted it enough.
“We kept at them and finally got the breakthrough with an excellent goal from Duffy.
“I’m so pleased for him. It will boost his confidence because he’s been a bit bitty of late.
“But we tried to give him a roaming role so he could get the ball on the ground and take the Stevenage defenders into areas they did not want to go.”
Laws acknowledged Scunthorpe’s fourth win in the last five home games was crucial in their bid to stave off relegation.
“When you look at how other results have gone you see how important this win was for us,” he added.
“But we have to concentrate on what we do and not bother with what is happening elsewhere. It’s in our own hands to climb towards safety.”
Bolton boss Phil Parkinson will check on the fitness of midfielder Darren Pratley before finalising his side to face Aston Villa at the Macron Stadium.