The Shots took the lead with just five minutes on the clock when Kirk Hudson's low cross picked out Danny Hylton at the far post, who with time and space slotted the ball past Barnet's Israeli goalkeeper Ran Kadoch.
Marvin Morgan then flashed a shot wide from just inside the area and in the early stages The Shots looked a threat with every attack. The Bees looked hesitant at the back while seemingly giving the ball away at every opportunity, encouraging the visitors and their support.
Hylton came close to doubling the lead midway through the half though saw his shot deflected wide for a corner, while the home side's only real threat came from the lively Albert Adomah, who tested Nikki Bull in the Shots goal on several occasions.
Kadoch had to be lively to prevent Ismail Yakubu heading into his own net as the home side were booed off at the break by their frustrated fans.
The second half would prove to weave a similar pattern with the visitors manufacturing a number of chances, notably on the counter-attack.
Hudson saw another low effort deflected wide for a corner, while Hylton hit the outside of the post with a fierce angled drive.
Andy Sandell somehow flicked over from Hudson's cross when it seemed easier to score, before they finally doubled their lead with 20 minutes remaining.
Scott Davies crossed at the second attempt and as Hylton flicked the ball on, Anthony Charles was free to head home at the far post.
Adomah hit the bar late on with a speculative effort, before Davies capped off a fine afternoon for the visitors when he ran through, rounded Kadoch and tapped home.