The Glovers took the lead after a very bright start. Green was brought down by Ricardo Santos as he raced into the box and the referee pointed to the spot after just 30 seconds.
Sam Surridge stepped up and placed the fired home, Craig Ross stood no chance despite guessing the right way.
The Bees failed to have a shot on target in the first half, Richard Brindley going closest when his effort from range skimmed the outside of the post.
However, Barnet came out after the break a completely different side but they would up against a goalkeeper in Jonny Maddison who was in inspired form and equal to anything thrown his way.
Simeon Akinola was the first to see a goalbound effort denied, substitute Mauro Vilhete had his effort with virtually his first touch tipped onto the post and David Tutonda’s hit from the edge of the box was hooked off the goal line when it looked destined to nestle in the bottom left corner.
Richard Brindley also had a couple of efforts, one of which produced the pick of the bunch of top-drawer saves from Maddison. Brindley lined up to shoot from all of 30 yards, the ball dipped and looked to be heading in just under the crossbar, but Maddison back-peddled and miraculously palmed it over the bar.
Yeovil did have opportunities, Santos having to clear Corey Whelan’s shot off the line with Craig Ross beaten.
As Barnet were piling forward in stoppage time, the Glovers caught the Bees on the counter-attack, Zoko getting around Clough before finishing into the bottom right corner from close range.
BARNET – Ross, Brindley, Clough, Santos, Watson, Weston, Akinde, Tutonda (Blackman ’83), Akinola (Vilhete ’72), Nicholls, Nicholson (Coulthirst ’50).
Unused – Legg, J. Taylor, Sule, Plavotic.
Attendace – 2,455 (71 Barnet)