STANLEY hot-shot Lee McEvilly fired home two goals to give the Reds play-off charge a huge boost against their promotion rivals.
McEvilly - who has now scored six goals in five games - finished from a tight angle in the eighth minute and pounced on a defensive mistake on the 57th minute to secure Stanley a vital three points.
Exeter, however, were ruing missed chances as they caught Stanley keeper Paul Crichton in inspired form.
They got past him once - in the 25th minute - when a Sean Devine cross was lashed against the underside of the crossbar by Dean Moxey and Jake Edwards was there to grab the loose ball and fire home.
Devine had several attempts to get past Crichton without luck, winger Les Afful was a handful in the second half and had four good chances kept out by the Stanley shot-stopper while Alex Jeannin's free header sailed into Crichton's arms.
"We realised that we couldn't afford to lose this game," said boss John Coleman. "The situation they are in they would have gone above us with two games in hand. A draw would have been a good result.
"I know they missed a couple of chances but so did we and on the balance of play, we deserved to win the game."