With fierce wind favouring Rossi Eames’ side in the first-half, the Bees took the lead just six minutes in.
Simeon Akinola made the most of wind assistance as his shot from range curled into the top corner, in what proved to separate the two sides at the break.
Boasting the backing of the conditions in the second half the Green and Whites dominated from the restart and deservedly levelled the scores with nine minutes remaining through Otis Khan.
With only one side looking like winning it the Glovers were denied a penalty in stoppage time, leaving Yeovil to frustratingly settle for a share of the spoils in London.
Looking to bounce back from defeat in midweek, Darren Way made two changes to the side that lost at Cambridge United.
Having served a one-match suspension, five-goal man Francois Zoko returned to partner top scorer Fela Olomola up front, forcing Sam Surridge to drop to the bench.
After a run of three games out of the side, Jake Gray returned to the starting eleven to take the place of Rhys Browne, whose move to the bench saw Keston Davies drop from the matchday 18.
Having travelled to the capital the Glovers weren’t the only visitors, as 60mph winds also spent the afternoon at the Hive as Storm Brian hit the UK.
In favour of the Bees in the opening 45 minutes, the hosts wasted no time in making the conditions work in their favour.
Entrenched in Yeovil territory, Akinola was firstly denied by a smart Artur Krysiak save before the Barnet striker picked out the top corner with some wind assistance just minutes later.
It took 15 minutes for the Green and Whites to enter Barnet territory in meaningful fashion and it almost brought an equaliser.
Jake Gray’s penetrative pass found its way to Khan who instantly transferred the ball to his right foot, before seeing a well-hit shot from the left of the box palmed over the bar by Craig Ross.
Although Storm Brian remained, Yeovil weathered the early Bees storm and produced another good chance to level the scores just before the half-hour mark.
Khan’s deep free-kick found its way to Fela Olomola, but Town’s top scorer could only volley over the bar from close range as the ball dropped over his shoulder.
Now coping with the swirling wind Krysiak remained untested until Mauro Vilhete’s header with 35 minutes on the clock, which the Polish stopper matched by tipping over the bar.
That chance marked the end of goal scoring opportunities, as the London outfit headed into half-time with a slender lead, knowing it would soon be their turn to face the wrath of Brian.
With the wind’s backing, Town took less than 10 minutes to produce their best chance of the match.
Having replaced Ryan Dickson at the break, Tom James’ floated ball into the box was flicked into the path of Olomola by Zoko, only for the striker’s shot to have the sting taken out of it by a sprawled Ross which allowed Nelson to clear off the line.
As rain was added into the windy mix the Glovers continued to press, and almost equalised in freak circumstances.
Nathan Smith aimed to loop a cross into the box from deep but watched on as the wind latched onto the ball and crashed it onto Barnet’s crossbar with Ross only able to watch.
Sparking excitement amongst the away fans, Rhys Browne showed neat skill to get to the by-line just a minute later, before his cutback was slammed just wide by Khan.
Becoming one-way traffic as the game ticked into the final 10 minutes Sam Surridge was introduced for Olomola and the changed paid off immediately.
Having harried Barnet into surrendering possession, Surridge poked a ball through for Khan who left two home defenders for dead before coolly slotting past a hapless Ross.
Sniffing the chance to complete the comeback Yeovil remained on the attack as the match ticked into stoppage time, and were left feeling short-changed when Browne went down in the box.
Seemingly tripped by a dangled Bees leg all eyes were on referee Andy Woolmer, who to the amazement of all only waved played on in what proved to be the last meaningful action of the game as both sides had to settle for a point.
Barnet: Ross, Santos, Nelson, Clough, Vilhete, J. Taylor, Fonguck, Tutonda, Campbell-Ryce (Amaluzor 88′), Coulthirst (Akpa Akpro 46′), Akinola (Mason-Clark 85′).
Bookings: Akpa Akpro 90′
Subs not used: McKenzie-Lyle, H. Taylor, Shomotun, Blackman.
Yeovil Town: Krysiak, Mugabi, Sowunmi, N. Smith, Dickson (James 46′), Gray, Bailey, C. Smith (Browne 64′), Khan, Olomola (Surridge 79′), Zoko.
Bookings: Sowunmi 50′, James 58′, Khan 85′
Subs not used: Maddison, Nelson, Worthington, Santos.