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. Exeter City beat Accrington on Friday night, but Plymouth Argyle and Torquay both lost.
Exeter City picked up a club record tenth away win of the season. There were also wins for Yeovil Town and Plymouth Argyle.
Yeovil Town won for the fifth game in a row after a 3-0 win over Brentford. There were draws for Exeter and Plymouth, but Torquay lost 2-1.