Matt Gill was the hero for the visitors, firing home the winner on 72 minutes as his side confirmed themselves as serious promotion contenders.
They now sit in the automatic promotions places following this win with two home games to come after success on their travels.
Paul Tisdale's men began strongly and carved out two clear chances in the opening 20 minutes as their passing game tore the home side apart.
The best opportunity fell to veteran striker Marcus Stewart, who fired his effort just wide from Danny Seabourne's headed throughball.
The Grecians came even closer on 26 minutes, when striker Adam Stansfield fired a rebound against Lee Harrison's post after the keeper had produced a fine save to turn away Richard Logan's header.
Barnet could only improve, and improve they did, with Albert Adomah beginning to pose the Exeter defence questions with his pace and trickery.
A chance finally fell to the feet of Adam Birchall from John O'Flynn's miscued shot, but the frontman scuffed his shot horribly over the bar.
Both sides found chances hard to come by after the interval but the breakthrough finally came as the game entered its latter stages.
Stewart found space in the area and his shot deflected into the path of Gill, who drilled a low effort, also via a deflection, past the helpless Harrison.
Barnet, determined to avoid another home defeat, desperately went in search of a late equaliser and it was their substitutes who nearly provided them with salvation.
Luke Medley broke free down the left and delivered the perfect cross for Cliff Akurang, but the burly forward could only power his header wide of the post.
The despair of the home fans at the final whistle was clearly audible but not as loud as the travelling Exeter contingent who headed back to the West of England with their side as clear promotion contenders.