Rovers took a welcome point despite failing to find the back of the net.
Green had the better of the chances at The Lawn, but neither side could take advantage of some sloppy defending to give themselves three points.
Gravesend had the best early chance when Onome Sodje fired over from the edge of the penalty area, while at the other end Michael Brough spurned Rovers' best chance.
From close range Brough failed to hit the target, firing high and wide after dinking past his marker on the edge of the box.
Rovers were value for money and are still five points clear of the relegation mire after tonight's point, but there is still plenty of work to do if they are to remain in the Conference next season.
With fellow relegation strugglers Altrincham beaten at home by Halifax Town, Green can be thankful of a point.
But a failure to convert, which has haunted them in recent encounters, will be a worry to their faithful supporters, over 500 of whom came out to watch tonight's frustrating draw.