The Millers, who were deducted 17 points at the start of the campaign, are already in positive points.
A double strike in the opening 10 minutes from Reuben Reid and Drewe Broughton went a long way to securing a sixth win of the season.
Former Bury goalkeeper Andy Warrington also saved an 80th-minute Andy Bishop penalty after Nick Fenton had fouled substitute striker Chris O’Grady.
Lively winger Reid opened the scoring after just two minutes when he latched onto an Andrew Nicholas throughball to slip home under Wayne Brown. Broughton doubled the visitors’ advantage in the 10th minute when his powerful header from 12 yards found its way inside the right-hand upright following Micky Cummins’ accurate right wing cross.
Bury came back into the equation when captain Paul Scott glanced home a Michael Jones corner, but it was too little, too late for the high-flying Shakers.