The hosts enjoyed the better of the opening exchanges but against the run of play Preston broke the deadlock in the 29th minute.
Scott Laird floated over a corner to the far post and Akpo Sodje stooped to head home his fourth goal of the season.
Adam Lockwood went close for Bury shortly after the restart, before Preston doubled their lead in the 67th minute with a goal again created by Laird.
His inswinging free-kick was this time headed home by defender Shane Cansdell-Sherriff.
Defender Joe Skarz nodded in Peter Sweeney's corner-kick in stoppage-time, but Preston comfortably held on.