Passmore headed Aber level two minutes into the second half, before the UWA student scrambled home the winner half an hour from time, after Aneurin Thomas saw a header rebound off the post.
The visitors had slightly more chances in an even first half and took a deserved lead 26 minutes in, Graham Evans converting a penalty after Passmore was adjudged to have fouled Andy Davies inside the area.
Jamie Hayes came close to doubling the lead four minutes later, his long-range drive saved well by Aber keeper Dave Jones.
Aber performed better following the interval, Thomas heading narrowly wide 10 minutes after Passmore's leveller.
The visitors pushed forward looking for the equaliser late on. However, the Aber defence, marshalled by the excellent Christian Edwards, held firm.