Damian Spencer's 26th-minute strike cancelled out Aaron Webster's 12th minute opener before Zola's late strike lifted the Brewers four places and five points clear of the drop-zone.
Shots keeper Jamie Young had to be alert early on, first to deny Webster and then to palm Greg Pearson's free-kick around the post, but John McGrath's resulting corner dropped kindly for Webster to prod the Brewers into the lead.
Paul Peschisolido's side responded positively and pulled level when Spencer cut in and rifled a fine strike past Adam Legzdins.
Pearson almost put Albion ahead at half-time, but their luck appeared to be out after the break until Zola latched on to Jacques Maghoma's pass to stroke past Young on 74 minutes.
And Pearson could have made it three with a late penalty after Darren Jones felled Maghoma but Young saved well to his left.
Source: PA
Source: PA