They made sure of the victory after the break, with David Bridges netting twice and sublime finishes from Andy Drury and Stacy Long completing the rout.
Stevenage will next face Blue Square South promotion hopefuls Dover.
Stevenage manager Graham Westley told BBC Three Counties Radio: "It was nice to get a good result, though I don't think we were at our best. We looked very ring-rusty.
"We laboured in the first half and probably fortunately went ahead. We didn't create as many chances as we would have liked to have done.
"When Drury came on and started expressing himself, the game really did change. He was a real handful for them tonight."