Halifax Town could be plunged into a relegation scrap after goalkeeper Craig Parry's blunder condemned the Shaymen to a fifth straight defeat.
Youth product Parry spilled Lee Phillips' right-wing cross into the path of striker Alex Meechan just five minutes into his home debut in place of suspended regular stopper Mark Cartwright.
Meechan tapped in from close range, but Parry redeemed himself on 24 minutes when he prevented the former Bristol City striker scoring his second of the game.
Meechan raced on to Martin Foster's throughball and tried to drill a low shot under the advancing Parry, but it clipped the keeper's trailing back leg and was eventually hacked to safety.
Halifax, who have not won a Conference game since beating Scarborough on Boxing Day, rarely threatened in a poor game.
The home side's best chance fell to on-loan Lincoln striker Rory May in the first half, but he shot tamely at goal following a mazy run past several Forest Green players.
The visitors, watched by a hardy band of about 20 travelling fans on a bitterly cold night, were in control for long spells and should have won more convincingly.
Alex Sykes blasted over on 37 minutes when a Scott Rogers cross was not cleared by the Halifax defence.
And veteran former Stockport, Chesterfield and Rochdale midfielder Damon Searle missed the game's best chance on 62 minutes when he headed straight at Parry from Phillips' free-kick, despite being unmarked inside the six-yard box.
But one goal was enough for Rovers to secure a vital win in their quest for survival and they have now leaped above Halifax in the Conference table.
Another couple of victories should see the Gloucestershire outfit finally put an end to their lingering relegation worries during a disappointing season that has failed to live up to their expectations, following a strong finish to last term.
Halifax, however, face a tough run-in with fixtures against promotion chasing Hereford United and Dagenham & Redbridge to follow and could face a nervy end to the season, despite starting the campaign among the favourites for a play-off spot.