Notts County condemned Stevenage to a second defeat of the season after the hosts missed an early penalty.
Krystian Pearce hauled down Craig Reid in the box after six minutes, but the Boro striker saw his effort from the spot saved by Stuart Nelson.
The Magpies took the lead in first-half stoppage time with Lee Hughes converting Mike Edwards' cross from close range.
Ben Burgess sealed the win after the break, heading in Jeff Hughes' cross.
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Stevenage manager Graham Westley tells BBC Three Counties Radio:
"We don't lose a lot here and in honesty, when you go down without a fight it's not a nice feeling.
"There was a lot of experience in their line-up and they used their shape wisely. [Gavin] Mahon was excellent in front of the back four.
"It's never nice for a player to miss a penalty but you miss chances in games and a penalty is just another chance.
"There were two red-card offences in the first half. I have tremendous regard for the referee, I really do, but I think both of those decisions were a red card offence. Had those decisions gone our way I think it would have been a very different afternoon."
Notts County manager Martin Allen told BBC Radio Nottingham:
"Five games in 14 days that is for us. Tuesday night away at Exeter, last week away at Juventus.
"What a fantastic achievement by these players, you just can't keep them down at the moment. The energy and the drive.
"It's been fantastic, a very special, special day."