Ian Thomas-Moore grabbed his seventh goal of the season to hand Tranmere a 1-0 victory at Bury and send them into the Johnstone's Paint Trophy Northern Area semi-finals.
Bury gave Rovers an early scare when Peter Gulacsi turned Nicky Ajose's 20-yard shot around the post, before Rovers took the lead with their first attack of the game in the eighth minute.
Shakers goalkeeper Richie Branagan came and missed Enoch Showunmi's cross, allowing Thomas-Moore to control the ball six yards out and volley in at the far post past two defenders on the line.
Tranmere dominated the early stages of the second half in terms of possession and territory but they were unable to turn it into chances.
Bury had come back into the game by the 55th minute when Thomas-Moore crashed a shot against the crossbar after being put through by Showunmi, only for the assistant referee to raise his flag for offside.
Lenell John-Lewis went close for Bury with a close-range header after 71 minutes before Les Parry's team survived a late free-kick to book their place in the next round.