Goals from Ben Futcher, Efe Sodje and Andy Morrell finished the match as a contest by half-time and Chesterfield could only manage a Lloyd Kerry strike in reply.
To make matters worse, the home side lost last season's top-scorer Jack Lester with a thigh injury early in the game and could be without him for several weeks.
Bury also had their top striker Andy Bishop sidelined by injury, but Morrell proved a more than capable deputy and the Shakers can look ahead with confidence.
They were by far the better side in all areas in the first 45 minutes and dominated once Futcher had connected with an overhead kick from eight yards after Sodje had headed back a free-kick.
Chesterfield were still coming to terms with the loss of Lester when Sodje increased Bury's lead, after Robert Page only half cleared a corner and the defender powered in on the right to fire low into the net.
The third goal was the best of all, with Glynn Hurst releasing Mike Jones down the left and he out-paced Page before setting up Morrell from six yards to put the game beyond Chesterfield.
At least the home side improved in the second half and there was a glimmer of hope for the supporters, who had jeered at half-time, when Kerry reduced the arrears.
Jamie Lowry made a strong run down the right in the 53rd minute and although he was clearly pulled back, referee Colin Webster played the advantage and Kerry found the net from 12 yards with a well placed shot inside Wayne Brown's left-hand post.
Webster resisted strong claims for a penalty when Jamie Ward went down under the challenge of Futcher, but although Chesterfield kept plugging away, Bury always looked in control.