In a tight first half it was Rovers who always looked the more likely to score and on-loan striker Julian Alsop duly delivered on the stroke of half-time.
The powerful hitman rose to meet a corner from Ben Harding and powered a header past the flat-footed keeper.
But instead of pushing on after the break the home side sat back and they were almost punished when Andrew Corbett went close with a powerful shot.
And Forest Green were indebted to defender Paul Wanless for clearing off his own line late on as they held on for a priceless victory.