The former United academy forward tapped home Lewis O’Brien’s inviting cross six minutes before half-time to hand the Red Dragons a deserved lead.
Phil Parkinson fielded two different line-ups across the match, while United also rotated heavily, with senior players including Harry Maguire and new signing Andrey Santos starting before a youthful side took over after the break.
Smith threatened throughout the opening half, while Bailey Cadamarteri and Nathan Broadhead also impressed.
In the second period, Danny Ward made key saves to preserve Wrexham’s advantage, denying Dan Gore and comfortably gathering Shea Lacey’s late effort.
The win marked Wrexham’s first pre-season victory of the summer and their second successive clean sheet ahead of the new campaign.