The first 15 minutes passed without either team dominating, although Bath had a slim lead thanks to a George Ford penalty.
Ford then missed another, but he made amends shortly after with an opportunistic drop goal.
Despite lots of bluster, the home side struggled to find their rhythm and were pinned back by an effective opposition attack.
The afternoon's first try came just before the break. After a powerful surge from Bath, the ball was then spread wide and Semsea Rokoduguni went over in the corner.
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Rokoduguni went over again and Ford converted to give the away side a dominant lead.