Captain Andy Robinson missed a first-half penalty, but made amends by grabbing the goal that secured Rovers' third win in a row.
Both sides started 2013 in sluggish fashion, as Robinson and Bury's Tom Soares were unable to hit the target with early opportunities.
Tranmere striker Michael O'Halloran found space inside the box, but his tame shot was saved easily by Bury goalkeeper Trevor Carson at the near post.
Tranmere were awarded a controversial penalty in the 43rd minute, but Carson made a stunning one-handed save to keep out Robinson's spot-kick.
The talismanic Rovers skipper continued to have a strong influence on the game in the second half and hammered a powerful shot against the Bury crossbar.
Eventually, his persistence paid off when he latched on to a through-ball from Liam Palmer and smashed a deflected shot past Carson.
Bury refused to give in but lacked punch up front, Tranmere goalkeeper Owain Fon Williams comfortably saving a neat shot on the turn from Steven Schumacher.