The visitors had the lion's share of the territory in the early stages, but fell behind in the 20th minute to an excellently worked free-kick routine.
Colin Potts' delivery was cushioned into the path of Gary Williams by Colin Little and as Williams shaped to pull the trigger, Rovers left-back Damon Searle produced a lunging challenge to knock the ball agonisingly beyond the reach of keeper Ryan Clarke. It was Altrincham's first goal of the new campaign.
Williams nearly doubled the Robins' lead, but pulled his shot across the face of the goal after combining well with Steve Hawes and Colin Little.
Paul Wanless was pulling the strings in midfield, setting up Rovers' only clear opportunity of the first period, which Alex Meechan clipped over the bar with Stuart Coburn out of position.
Altrincham doubled their lead three minutes after the break in controversial circumstances.
Little looked a couple of yards offside as he received an intelligent pass from Potts before advancing to the byline to delivered an inviting cross which Potts headed towards the bottom corner. Clarke produced an excellent save but Potts bundled the rebound home in slightly fortunate fashion.
Forest Green responded well and had a couple of good opportunities but both skipper Jon Richardson and Wanless were wide of the mark before Altrincham's Val Owen was penalised for bundling over Lewis Haldane, who had been on the pitch less than 60 seconds.
Referee Lewis pointed to the spot and Wanless sent Coburn the wrong way from the resulting penalty kick.
Altrincham held on for the remaining 20 minutes, although Scott Rendell appeared to have equalised for the Gloucestershire side before his strike was overruled by the linesman flagging for offside.