Chesterfield kept up their bid for a promotion play-off place as Peter Leven kept his cool from the penalty spot.
Leven settled the outcome on half time after referee Anthony Taylor had pointed to the spot following a foul in the box by Andy Parrish on Jamie Winter.
The chances of a second-half comeback from Bury were reduced just before the hour when Paul Scott fouled Steve Fletcher and collected his second yellow card.
And their last hope of snatching a point disappeared when Nicky Adams' shot was blocked in the final minute.