Carlisle United scored two early goals and held on for all three points despite a strong comeback from Bury.
Lee Miller opened the scoring from the penalty spot after Brad Potts's trickery drew a foul from Shakers defender Efe Sodje.
Matty Robson then doubled the Cumbrians' advantage, driving home Frank Simek's cross with his left foot.
Stephen Schumacher pulled one back for Bury, heading home Sebastien Carole's cross, but Carlisle held on to win.
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