Victory also meant Rovers moved out of the relegation zone for the first time since Jim Harvey took over at the helm of the Gloucestershire club earlier in the season.
Rovers deserved their third home victory of the campaign, but should have won by a much greater margin.
Alex Meechan spurned a host of gilt-edged chances and when Rovers did manage to get their efforts on target they found Town keeper Ben Hamer in inspirational form.
Despite dominating the game they had to wait until ten minutes from time to make the breakthrough.
Charlie Griffin stuck the first goal of his second loan spell at The Lawn.
The Wycombe Wanderers striker was also loaned to Rovers two years ago but marked his seventh appearance for the Conference club this campaign with the winning strike in the 82nd minute.
Meechan made amends for his earlier mistakes by picking out the hitman and he found the back of the net from 18 yards.
Towards the end, Crawley came more into the match and home keeper Steve Williams had to be alert to palm away an effort from Scott Rendell.