The Glovers were on the back foot from the start but broke to take the lead after 17 minutes. Nathan Jones lobbed a free-kick over the defensive wall and Kieran Agard beat goalkeeper Trevor Carson with an overhead kick after confusion in the Bury backline.
Yeovil held their lead then without much difficulty until the 43rd minute when Andy Bishop and Giles Coke created space with a clever one-two for Coke to slip the ball past Jed Steer. Coke almost scored again in first-half stoppage time.
Bury continued where they left off in the second half and were clearly the more effective side. They took the lead after 67 minutes when Peter Sweeney's right-wing corner was headed firmly home by Liverpool loanee David Amoo.
Yeovil conceded another after 84 minutes when the Shakers quickly cleared a free-kick and Sweeney beat the last defender to finish easily.