Bury striker Ryan Lowe's 50th goal for the club helped condemn Sheffield Wednesday to a second straight defeat.
Lowe met David Worrall's inch-perfect cross with his head to put Bury ahead on seven minutes.
After the break Damien Mozika doubled their lead when he stroked into the corner from a Joe Skarz through-ball.
Reda Johnson had a goal ruled out for the Owls for a foul but Chris Sedgwick pulled one back with a curled 20-yard strike which went in off the crossbar.
VIEWS FROM THE DRESSING ROOM
Bury manager Richie Barker told BBC Radio Manchester:
"I'm ever so pleased with the result but even more pleased with the performance.
"A fantastic response and I think good teams never get beaten twice in a row and I think the fact we've done that tonight proves we're a good team.
"We need to continue to pick up points, but in terms of tonight we accept what we've done and what we've got, and now move on."
Sheffield Wednesday manager Gary Megson told BBC Radio Sheffield:
"Where this has come from, I don't know. From looking such an accomplished side on the first day of the season we looked really poor tonight especially in the first 45 minutes.
"Whenever we play it will, certainly away from home, be their biggest game of the season. It's their big scalp of the season and we've got to fight fire with fire.
"If we lose again it's relegation form - it's that close. if we win again then that will get us back into that but we won't win any games performing with that kind of football that we played tonight".