The home side made a whirlwind start with centre-half Ben Futcher scoring a second-minute opener before Glynn Hurst gave Bury a two- goal cushion in the 11th minute.
Hurst grabbed another on the stroke of half-time and the Shakers comfortably held on to stretch their unbeaten run to four.
Richie Baker came in for Bury for the injured Brian Barry-Murphy (back) while Simon Richman replaced Scott Brown in the Vale midfield after coming off the bench to score the winner against Grimsby last week.
But it was clear from the outset it was going to be Bury's day as Futcher showed great composure to open the scoring.
Vale cleared a corner as far as Stephen Dawson, who swept in a right-wing cross which was flicked on by Hurst and Futcher took one touch before coolly slotting the ball past Lee Anyon from 16 yards.
Bury winger Elliott Bennett then combined with Hurst to release Andy Bishop in the right channel and his vicious strike forced Anyon to tip the ball over.
But the trio soon combined again to carve open the Vale defence and double Bury's advantage.
Bennett's crossfield ball from the left was chested down by Bishop into the path of Hurst, who held off the challenge of Lee Collins to clip the ball over Anyon from 12 yards.
Vale regrouped and Glover twice tried his luck from the edge of the box, first testing home keeper Wayne Brown before dragging a similar effort harmlessly wide.
Bury remained in charge, though, with Bishop heading narrowly over from a Hurst cross before Hurst stabbed the ball home in first-half stoppage time after Paul Scott knocked down Jones' right-wing corner.
Richards went close for Vale after the restart, but Anyon turned a Bishop strike round the post and only a goal-line block from Gareth Owen stopped Bennett extending Bury's lead.
Anyon then produced another fine save to beat away a 75th-minute strike by Bishop and prevent Bury making the victory even more emphatic.