Both sides were keen to get onto the front foot in the early stages, but it was Rovers who looked most threatening as Matty Taylor fired an effort wide before Jake Gosling struck a shot straight at Steve Arnold.
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It was Taylor who broke the deadlock inside 17 minutes as he drifted into space on the edge of the box before finishing calmly against his former side.
The visitors grew in confidence after taking the lead as Forest Green were forced to survive long spells of pressure in a frustrating first half for the hosts.
Bristol could have doubled their lead before the break, but Arnold made a fine save to keep out Taylor after a clever pass from Tom Lockyer.
Taylor's movement continued to cause problems for Forest Green in the second half, but he wasted a promising chance with a wayward effort.
Despite being in control for long spells of the match, Bristol were put under unnecessary pressure in the closing stages when Ellis Harrison picked up his second yellow card for a foolish challenge on Arnold.
Forest Green had chances to get back on level terms late on, with Aarran Racine seeing a header cleared off the line before Charlie Clough struck the woodwork as Bristol held on in stoppage time.