The big Ivorian struck in the 79th and 85th minute to complete a stirring fightback after Aaron McLean's first half brace had given the Bees a two goal interval lead. The Glovers, lacklustre in the first half and for parts of the second half, escape with a point that lifted Darren Way's side off the bottom and into 23rd place.
The manager made two changes to the side that lost 3-2 to Oxford United in the Johnstone's Paint Trophy on Tuesday night. Ryan Dickson came in at left back for Nathan Smith while Ben Tozer also dropped to the bench, Shaun Jeffers coming in up front.
And it was Dickson who nearly opened the scoring on five minutes. His viciously in swinging corner almost caught new Barnet loan keeper Ian Lawlor unawares and he ad to clear desperately from off his line. Yeovil continued their bright start with both Matt Dolan and Jeffers have shots blocked one after another but Aaron McLean fired a warning shot across Yeovil's bows, and towards their goal, but Connor Roberts cleared off the line superbly.
It was only a brief escape though as on seventeen minutes, Barnet took the lead. Jakub Sokolik was penalised for a foul on McLean and the experienced striker fired an unstoppable free kick into the top corner of the net.
Yeovil tried in vain to get back into the game but their efforts were either weak or off target or both. Jeffers poked a shot at Lawlor, Josh Sheehan curled a shot well wide and then Harry Cornick sliced a left foot shot wide on the 44th minute. Then, just as the half time whistle was about to blow, McLean was played through springing the offside trap and finished calmly into the corner.
After the break, Darren Way brought Tozer on for Sheehan but the pattern of play didn't change much, Martin Allen's men were on top and there seemed little chance of the Glovers getting much from the match. Zoko turned and shot but his attempt was blocked, Roberts shot inches wide and though Luke Gambin shot wide, Chris Weale in the Yeovil goal had little to do except for goal kicks really.
Zoko then went even closer on 77 minutes when Lawlor denied the striker with his legs but a minute later, he pulled a goal back when Roberts crossed and he flicked a diving header past the keeper and into the corner.
Bird headed wide from a cross by sub Iffy Allen, making a rare appearance off the bench but on 85 minutes, the equaliser arrived and in some style. The ball was cleared from a cross to the edge of the box where Zoko swivelled and struck a stunning effort past Lawlor.
Late on Yeovil almost grabbed a sensational winner when Allen's pace down the left saw him cut inside and fire towards the corner of the goal but Lawlor saved well. Five minutes of stoppage time couldn't separate the two sides so points shared at Huish Park.