Town broke the deadlock at the Lamex thanks to Aaron McGowan's sensational half-volley on 17 minutes before Mitch Pinnock's powerful strike gave them breathing space.
Former Town man Chris Lines did pull one goal back but it came too late for the struggling hosts to avoid another defeat.
"It was good to bounce back after the weekend," said Brady. "I felt we started well and we were in control of the game for a lot of it.
"We moved the ball well and scored with Aaron's goal and that gave us a really good start and then we controlled the game for large periods.
"They threw everything they could towards us at the end and there were a few tough moments but apart from that, it was a good night and a big win.
"Stevenage gave their manager everything and they are fighting for their lives at the moment so you just have to go and get a result somehow, someway, and in the end we stood strong and that was positive."