Eighteen-year-old striker Jake Robinson - on loan from Brighton - and midfield man David Lee netted the goals which decided a frenetic clash.
Exeter hit back with a last minute goal from Gary Sawyer and set up a tense finale, which had the 2,579 crowd on the edge of their seats.
But the Shots held on to make the play-off picture all the more interesting.
The home side started a brighter and but for a timely offside flag would have been ahead on just two minutes - Jon Challinor's effort ruled out after keeper Paul Jones spilled a shot from home debutant Adrian Caceres.
Exeter had their moments also in a rollercoaster first half, but found Shots keeper Nikki Bull in form, making a mockery of the slippery conditions.
The real chances, though, were coming at the other end with Lee somehow not managing to register a shot when just six yards out.
A goal had to come and on 31 minutes it duly arrived for the hosts. A fine one-touch move down the centre ended up with Caceres helping the ball on to Robinson who slotted coolly past Jones.
With the goal, the game opened up further and either side might have added to the scoreline.
Exeter came closest with Bull producing the save of the match to deny Les Afful from point-blank range, while Will Antwi was forced to clear from his own goal-line to keep out Andy Taylor's shot.
The Shots then doubled their lead against the run of play when referee Mike Yerby spotted a handball in the box and Lee stepped up to rifle home the resulting spot-kick.
The visitors kept plugging away and were worthy of their 90th minute goal from Sawyer, but despite much pressure late on it proved to be only a consolation.