Braces for Danny Newton and Alex Revell secure victory for the hosts, Shaq Coulthirst’s solo effort only a consolation.
It was the Bees that started the match on the front foot, Ryan Watson hitting the crossbar with an in-swinging corner within the opening 10 minutes.
Stevenage took the lead just a minute before the break, Newton getting on the end of Ben Kennedy’s cross to head home at the far post.
After the restart, Newton hit an unstoppable volley from 25 yards out to double the hosts advantage shortly after the hour mark.
Revell made it three five minutes later when he beat Craig Ross with a low effort.
Shaquile Coulthirst pulled one back with a great solo run before hitting a left footed effort across the face of goal into the bottom corner giving Tom King no chance.
Just minutes later it was four when Newton raced down on goal before playing in Revell to secure the points.