Player-assistant manager Butler raced from his goal for a ball he couldn't reach and Meechan ran to meet it lobbing the ball into an empty net from 16 yards.
Halifax had opened brightly with a flurry of chances inside the opening minutes.
The Shaymen's top scorer Brian Quailey kept the Forest Green back four busy, winning every ball in the air and attacking them at every opportunity.
In the sixth minute he ran clear on goal before firing his shot at keeper Steve Perrin.
Both Adam Quinn and Shaun Garnett should have scored for Halifax with headers but they failed to hit the target.
Finally the breakthrough came in the 35th minute when Halifax player of the year Craig Midgley found an unmarked Andy Farrell in the six-yard box and he headed into an unmanned net.
Forest Green did creep back into the game once they were behind but they were unable to find a way past a solid Halifax defence. The second half saw Rovers attack Halifax's slender lead from the off.
In the 54th minute Meechan missed a clear chance to level the score but his diving header sailed over the bar.
But then Butler's error led to Forest Green getting the goal their battling performance richly deserved.
Halifax manager Chris Wilder watched the game from the stands because of a three-match touchline ban for dissent. He said: "I am gutted it feels more like a defeat, we started well but haven't got a natural goalscorer or killer instinct." Colin Addison, the Rovers manager was delighted with the way his team has performed this season, he said: "I am pleased with our second-half performance. Overall we have had a magnificent season."