Striker Adam Boyes scored for the third consecutive game as Barrow recorded their first Blue Square Bet Premier win of the season at Bath.
The hosts enjoyed the best of the first half with Lewis Hogg and Lee Phillips denied by Bluebirds keeper Danny Hurst.
Phillips had a second good chance just after the break from an Alex Russell corner but the striker fired just wide.
Boyes made Bath pay when he met Jack Mackreth's cross six yards out and shot low into the bottom corner.
Bath City: Garner, Simpson, Jones, Preece, Stonehouse, Hogg, Mills (Rollo 81), Connolly, Cook (Murray 63), Russell, Phillips. Subs Not Used: Matthews, Webb, Burnell.
Booked: Phillips, Mills.
Barrow: Hurst, Smith, Mike Pearson, Quinn, Skelton, Rutherford, Almond (Hulbert 58), Ferrell, Mackreth, Cook, Boyes. Subs Not Used: Shaun Pearson, Bolland, Owen.
Ref: Michael Bull (Essex).