Stevenage winger Lucas Akins's first-half goal condemned Peterborough, without top-scorer Britt Asombalonga, to a fourth successive defeat.
Akins curled home from 20 yards midway through the first half before Hogan Ephraim almost equalised, his close-range shot well saved by Chris Day.
Stevenage played the final 30 minutes without Jimmy Smith, who was dismissed for two bookable offences.
And they held on despite Posh skipper Tommy Rowe's volley clipping the bar.
VIEW FROM THE DRESSING ROOM
Stevenage manager Graham Westley told BBC 3CR:
"I thought we got what we deserved. We came with a strong game plan, and got on the front foot. Certainly when we went down to 10 men it was a back-footed performance that we had to put in, but very disciplined, very hard working and a thoroughly deserved three points.
"We took the game to them. We were the side that looked likely. There was a moment or two for them, but we were the dominant force."
On Jimmy Smith's red card: "I thought it was fair enough. I think the first yellow, you can't have any arguments, and then he stepped across the line for the second. I think the two yellows were probably deserved by him.
"They got themselves into a position where I think the referee was under a lot of pressure. The referee under that pressure was allowing things to go."
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