Late Alex Nicholls strike hands Barnet all three points
Barnet scored with their only shot on target to snatch a 1-0 win away at Yeovil.
The Glovers had dominated throughout, hitting the crossbar twice, but failed to make the breakthrough as substitute Alex Nicholls punished them late on.
Yeovil came close twice in the opening 10 minutes as Ryan Hedges and Otis Khan both drew saves out of Jamie Stephens, and then nearly broke the deadlock early in the second half when Kevin Dawson's long-range deflected effort was well parried by Stephens.
Six minutes later, the hosts thought they had their goal when Barnet failed to clear a Ryan Dickson cross and Tom Eaves' header beat Stephens, but cannoned off the bar.
And the woodwork saved the Bees for a second time when Khan's half volley flew into the frame of the goal with the keeper well beaten.
It looked as though it was only a matter of time before the Glovers found the net, but Nicholls grabbed a shock opener for Barnet six minutes before the end as his low drive beat Artur Krysiak to leave Huish Park stunned.
Khan had the chance to equalise in the final minute, but shot straight at Stephens as the Glovers left the field wondering how they had ended the game on the losing side.