Lee Molyneux's early strike proved enough to maintain Stanley's Football League status with a game to play.
The Reds travelled south with their survival hopes in their own hands and they did not let it slip, sparing themselves a nervy final day.
Stanley put in another resolute performance to stretch their unbeaten run to five and go four points clear of the drop zone with one game left.
The Reds silenced a bumper home crowd by taking the lead in just the second minute, Molyneux producing another stunning strike from long range.
The left midfielder tried his luck with a 40-yard free-kick and although keeper Steve Mildenhall got a hand to it, he could only help it into the top corner.
After scoring one goal in his first 30 games for Stanley, Molyneux's now scored eight in 12.
That early strike rocked Rovers and they took time to fashion their first effort on goal, a 25-yard strike by Tom Parkes straight into Paul Rachubka's midriff.
Rommy Boco then volleyed wide for the Reds from just outside the box while Oumare Tounkara was inches from heading in a Rovers corner.
Another corner then deceived Peter Murphy and Stanley were relieved to see Eliot Richards head over from close range.
Richards and Boco both had shots deflected wide before the break, while Ollie Clarke volleyed narrowly over from a Rovers free-kick.
Boco spurned a great chance to double Stanley's lead after the interval, sending a free header wide from just six yards.
Fabian Broghammer fired over as the Pirates pushed for an equaliser, while Rachubka comfortably dealt with efforts by Richards and substitute Ryan Brunt.
But for all their possession, the hosts just couldn't prise open a determined Reds' defence.