Bristol won the West Country derby in torrential rain at Brickfields.
George Watkins and Redford Pennycook crossed the line for the visitors either side of half-time, sealing a first away victory since early September.
Albion scored a consolation try through Rhodri McAtee in the final minute.
Yeovil Town won for a club record 8th time in a row. Bristol Rovers also won, Cheltenham drew and Bristol City lost in the Severnside derby.
There were wins today for both Bristol clubs and Yeovil Town. Swindon Town could only draw and Cheltenham Town slipped to defeat.
Bath have beaten West Country rivals Gloucester 32 - 5 in the LV= Cup.