Sean Canham's goal downed Barrow as Bath secured their first Blue Square Bet Premier away win of the season.
Canham pounced on Paul Stonehouse's cross to tap home from close range and bag his third goal in five games.
Glyn Garner did well to deny Andy Cook an equaliser for the hosts, who had not lost at home in their last 13 games.
Scott Murray almost made it 2-0 but was denied by Shaun Pearson, while Adam Boyes had a chance saved by Garner late on as Bath held firm.
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Bath City defender Jim Rollo told BBC Radio Bristol:
"Marc Canham asked on the way up here if I realised that this was the last ground we managed to win away from home at. If I remember rightly we scored a free kick that missed everybody and went in the net when we were up here last time.
"Tonight Sean managed to get a lucky finish or a bit of a fluke but after going 1-0 up the lads had something to hold onto and it was a good win in the end.
"It was a night to put the work in and put the ball in good areas and I think we did that."