Stanley suffered their first defeat in six games after Ryan Dickson scored the only goal at Huish Park.
The Reds had bad memories of their trip to Yeovil last season when they missed out on the chance to play Manchester United after losing the FA Cup second round replay and it again proved an unhappy ground for John Coleman’s men.
Dickson struck in the 64th minute as it boosted their survival hopes while the Reds remain in fourth spot in League Two.
Stanley had the first strike on target on four minutes when Piero Mingoia’s cross found the head of Matt Crooks but his effort was comfortable for keeper Artur Krysiak.
Krysiak also kept hold of a Billy Kee effort in the opening 20 minutes while Tahvon Campbell was lively for Yeovil, volleying one shot wide and curling the other into Ross Etheridge’s arms.
Kee thought he had scored the opener on 27 minutes when he got on the end of Mingoia’s cross and his header was destined for the top corner but Krysiak did brilliantly to claw it out.
Stanley came more into the game towards the end of the half with one close range Kee effort being deflected wide and then, from a Sean McConville free kick on 42 minutes, Krysiak missed the ball but striker Kee could only head it wide at the far post.
Krysiak tipped a Crooks effort wide at the end of the half as it remained goalless at the break.
Yeovil boss Darren Way made a double substitution at the interval and they pressed without troubling Etheridge while, 10 minutes into the half, Shay McCartan entered the fray for Rommy Boco for Stanley.
It was then the Glovers scored the only goal of the game on 64 minutes when they cut open the Stanley defence with a swift passing move and sub Francois Zoko found Ryan Dickson who clipped the ball past Etheridge.
McCartan almost got the Reds back in it four minutes later but his fierce shot was saved by Krysiak while, at the other end, Etheridge pushed out a Campbell drive.
Sub McCartan was lively for Stanley testing Krysiak again as Coleman put on Marcus Carver and Adam Buxton as the Reds searched for an equaliser which just wouldn’t come for the visitors.