The Grecians scored the first opposition goal at Yeovil since Portsmouth's equaliser against Town in February, as Ollie Watkins volleyed past former Exeter keeper Artur Krysiak.
And the win was sealed when Jake Taylor made it two in the second half as the Devon side left Huish Park with all three points, as Town lost at home in League Two action since November.
But despite Yeovil starting the game brightly, it was the visitors who took the lead on 15 minutes. After a one-two with teammate Holmes on the edge of the area, Watkins made space to fire low past Krysiak in front of the home terrace.
The opener was against the run of the play, and despite conceding their first goal for 472 minutes at Huish Park, Town looked to get back into the game straight away. Several crosses flew into the Exeter area, but agonisingly Yeovil failed to capitalise.
The Grecians nearly made it two when Taylor's drive from outside the box hit Krysiak's right-hand post, before Stockley's acrobatic volley flew just over the bar as the visitors looked to double their lead.
It was a case of Yeovil having more of the ball but the visitors having the more clear-cut chances. Town had a big opportunity to equalise with ten minutes of the half left as a flowing move found Zoko with only the goalkeeper to beat, but the Ivorian shot straight at Bobby Olejnik from ten yards out.
As the game restarted, Yeovil started with real verve. Kevin Dawson ran at the Exeter defence and shot with the outside of his foot, but his effort in front of the home terrace went just wide of the Grecians' goal.
Darren Way looked to get his side back into the game, and introduced the attacking threat of Harry Cornick and Jack Compton for Ben Tozer and Tahvon Campbell within ten minutes of the restart.
Stockley again went close to doubling the lead for the visitors with a 25-yard free-kick as his shot flew towards the top corner, but Town keeper Krysiak gathered well.
But the Grecians made it 2-0 with twenty minutes to go. Taylor wriggled down the right-hand channel and his first shot was saved well by Krysiak. But the winger was first to the rebound and his shot smashed into the net to send the travelling supporters into raptures.
The pitch was becoming more and more slippery as the hail bucketed down, and Exeter very nearly made it three. As the ball came out to Taylor from a corner, his shot cannoned into Krysiak, but this time the rebound was kind and the ball was cleared.
Ryan Bird was brought on as Way made his last throw of the dice, and the striker went close to halving the deficit as he met Compton's corner, but the Exeter defence got in the way to stop it going in.
Compton forced Olejnik into a fine save as the clock ticked down towards full time, but Exeter and their vocal travelling support left as the first away side to win at Huish Park in the league since Wycombe in November.
Yeovil: Krysiak- Roberts, Sokolik, Smith, Dickson- Tozer (Compton 49'), Shephard (Bird 75'), Walsh- Dawson, Zoko, Campbell (Cornick 53') .
Subs not used: Weale, Dolan, Lacey, Lita.
Exeter: Olejnik- Moore-Taylor,Woodman, Brown, McAllister- Noble, Harley, Holmes, Taylor (Davies 85')- Stockley, Watkins (Nicholls 83').
Subs not used: Ribeiro, Wheeler, Tillson, Pym, Grant.
Booked: Watkins 9', Holmes 52'