Scott Laird's goal dented Sheffield Wednesday's promotion hopes to give Stevenage a fantastic away victory.
Wednesday had the better of the early openings, both Chris O'Grady and Jermaine Johnson having efforts well saved by visiting keeper Chris Day.
And Stevenage took advantage when Joel Byrom's corner found its way to Laird, who turned in.
The hosts continued to press but Day was at his best to deny David Prutton and help his side to the three points.
Sixth-placed Stevenage's win cements their place in the League One play-off zone, while Wednesday drop to third, overtaken by local rivals Sheffield United, who won at Huddersfield.
VIEW FROM THE DRESSING ROOM
Owls boss Gary Megson told BBC Radio Sheffield:
"It's a disappointment. We've had 11 shots to their two. I think we've had 10 corners to their two and we've come out having lost 1-0.
"The biggest disappointment I've got at the moment is, out of the last six games we've cost ourselves nine points from defending set-pieces. Free kicks down at Exeter, a corner today, a free kick against Charlton. You wouldn't mind too much if all you did was send them out and say get on with it, but we practise them the day before each game.
"Set-pieces are such an important part of football and we're getting people switching off and at the moment it's killing us."
Stevenage manager Gary Smith told BBC Three Counties Radio:
"The guys were hungry to play and full of energy and enthusiasm.
"The opening exchanges probably showed that Sheffield Wednesday had the lions share of opportunities and pressure.
"But when you come to a place like this you don't expect to be runaway winners.
"There was some quality tonight that needed to be shown - that we needed to have in abundance - and I think it was there for all to see."