Former England Under-21 international Jamie Stuart scored the goal that dumped Stoke City out of the Worthington Cup at the opening hurdle.
Stuart's header from a superb Jon Newby cross came after 56 minutes and was no more than the Third Division outfit deserved.
Indeed, the Shakers could easily have won by a wider margin, as George Clegg had a shot cleared off the line by Clive Clarke while defender Danny Swailes smashed a header against the crossbar from a Terry Dunfield corner.
City almost sent the match into extra-time, but Glyn Garner kept his first clean sheet of the campaign with an outstanding save from Chris Iwelumo's 88th minute header.
By that time the visitors were down to 10 men due to Brynjar Gunnarsson's reckless two-footed challenge on Michael Nelson.
Stoke boss, Steve Cotterill, had no complaints with the red card saying: "We've got to make sure it doesn't happen again though the lad could have got up a bit quicker.
"Sometimes you have to hit the bottom before you can bounce back and good luck to Bury. Every dog has its day and they've just had theirs."
Bury player boss Andy Preece said: "This win is great for me because we've never really had a Cup run while I've been here. Normally we go out in the first round! "I'm just disappointed that the fans didn't turn out to support out. So it looks as though we'll need to be drawn away in the next round to try and get in a bit of money."