In a tense and nervous match it was the visitors who opened the brightest. Nick Crittenden had an early shot blocked for the Shots while at the other end keeper Nikki Bull saved well from Gary Holloway.
Boro shot-stopper Craig Holloway then saved Tim Sills' shot, and when Jonny Dixon pounced on the rebound, defender Nick Burton was on hand to block.
Ali Chaaban then broke forward for Boro, but Will Antwi, who was enjoying another fine game, tackled well to clear the danger.
Just before the half-hour mark, the Shots took the lead when Darren Barnard fed Sills. He set up Dixon and the young striker wrong-footed the keeper as he slotted the ball into an empty net.
Craig Holloway was called on to make further saves from Sills' deflected shot and Dixon who pounced on the rebound, before Steve Watson headed over.
The Shots got the best possible start to the second half by doubling their lead just four minutes in.
A neat one-two between the front pair saw Dixon whip the ball in for Sills to head home.
Bull spilled a shot from Robert Traynor at the other end but managed to block Paul Harkness' follow-up effort.
As the Shots looked to increase their lead, Craig Holloway saved from Sills. When the striker got hold of the loose ball, Tony Taggart was on hand to clear off the line.
With just three minutes left, Boro managed to pull one back when Adrian Deane's cross was nodded home by the unmarked Michael Charles.
However, it was too little, too late and in truth the Shots had done more than enough to earn the derby win.