Stone's winner on 68 minutes came after a defensive lapse had seen the striker challenge the keeper, come away with the ball and finish into an empty net while the visitors claimed a free kick. The result sees the O's move into fourth spot, a point behind leaders Wellington.
Manager Dale Dempsey made just one change to the side that narrowly beat Roman Glass on Wednesday evening, Lewis Parker coming into midfield in place of Matt Curnock who took a place on the bench.
Radstock started the brighter but their finishing lacked precision with Craig Wilson twice missing the target inside sixty seconds. Oldland's skipper Gary Shorney was then taken out late by Josh Witcombe who was booked for the foul, O's not producing anything from the set piece.
Oldland's final ball was often bouncing out of reach of striker David Stone but one he did get hold of saw him burst into the box and brought down, the referee waving away appeals for a spot kick. On 36 minutes, O's keeper Josh Dempsey had to get down quickly to his right to push an effort from James Rustell on to the post, a narrow squeak for the home side who then saw Tyrone Fudgell's shot blocked on its way towards goal.
After the break, Josh Witcombe was well wide with a left footed shot and O's broke from the goal kick, forcing a corner from which Ashley Bernard headed wide. Shorney then played in Fudgell from the right but the midfielder's shot was parried strongly by Dan Nolan in the Miners goal.
The pressure was telling and on 68 minutes, along came the winner. Fudgell played a precise ball over the top that set up a 50/50 challenge between Nolan in goal and Stone bearing down on him. The collision left Stone with the ball and he finished clinically while Radstock claimed for a free kick that never came.
Shorney had two opportunities to score before then going really close with a rasping effort that went just over the bar. As O's looked for a second to kill the game, sub Matt Curnock hit a rising shot over and Stone saw his shot smothered by Nolan for a corner.
In the end, the home side had to be satisfied with a single goal victory, their third successive one in league and cup this season. Next up at Castle Road is Chippenham Park on Wednesday evening, kickoff at 7.30pm.