Andy Morrell scored twice in two minutes to give Wrexham a first Blue Square Bet Premier win of the season.
After spurring a host of first-half chances, the Dragons finally made their dominance count with 13 minutes to go when Morrell tapped in at the far post.
The striker struck moments later with sublime left-footed half-volley from Adrian Cieslewicz deep cross.
Chris Maxwell's superb save from a Lee Phillips header ensured Wrexham left with the points and a clean sheet.
Bath City: Garner, Simpson, Jones, Preece, Stonehouse, Murray (Cook 71), Burnell (Mills 65), Watkins, Russell (Connolly 63), Hogg, Phillips.
Subs Not Used: Rollo, Webb.
Booked: Jones, Phillips.
Wrexham: Maxwell, Obeng, Creighton, Knight-Percival, Ashton, Harris, Fowler, Tolley, Morrell, Wright (Cieslewicz 64), Speight (Pogba 63).
Subs Not Used: Mayebi, Clarke, Taylor.
Goals: Morrell 78,79.
Ref: Warren Atkin (West Sussex).