The Stags were certainly good value for victory as Shakers boss Graham Barrow offered no excuses for his team's dismal display at Gigg Lane.
Adam Murray gave the Stags a deserved first half lead with Adam Rundle completing the win eight minutes from time. Rundle, who only signed from League of Ireland outfit Dublin City last month, was arguably the visitors' man of the match.
It was Rundle's superb cross field pass that led to Murray netting his fifth of the season with a 20-yard half volley.
Murray returned the compliment in the closing stages as Rundle fired home from close range for his first goal in Mansfield colours.
In contrast, Bury rarely troubled Stags keeper Kevin Pilkington, whose main work was to field a succession a misdirected corners and free kicks and, when Bury did manage a rare attempt on goal, there was no venom behind the shot.
Fraser McLachlan and Richie Barker should have broke the deadlock with first half headers, but it was third time lucky when Murray gave keeper Andy Marriott no chance with his blistering drive.
Bury, giving a whole debut to on-loan striker Bas Savage, were marginally better after the interval and they were unfortunate not to profit from a goalmouth scramble in the 60th minute.
Mansfield were always lively on the counter attack and Murray forced Marriott into a good save in the 61st minute.
Marriott also tipped a Rundle centre onto the cross bar as Bury's defence struggled to cope and, while there was a suspicion of offside for Rundle's goal, there was no denying Mansfield would have won even had it stayed at 1-0.