After an assured start, Town took the lead inside the opening 20 minutes when home keeper Benjamin Buchel’s clearance was charged down by Ben Whitfield, which sent the ball looping into the net.
After a spell of Bees pressure, the hosts equalised when Ryan Watson’s corner was headed home by captain Michael Nelson, despite the final touch seeming to come off a Yeovil man.
Deep in the second half Watson’s free kick from almost halfway somehow rolled into the net and look to have given Barnet three points, but Shephard scored a timely first senior goal in stoppage time to earn Town a point.
Having left Morecambe with an impressive three points at the weekend, Darren Way was forced into one change from the side that started at the Globe Arena.
Alex Lawless, who picked up a hamstring injury up North, was replaced by scorer of Saturday’s stunning opener Matt Butcher while Brandon Goodship returned on the bench following a foot injury.
The only League Two fixture on Wednesday night, managers and scouts from across the division descended on the capital and almost saw the hosts take the lead with seven minutes on the clock.
Simeon Akinola’s cross to the back post picked out the league’s top scorer John Akinde, but the striker’s simple finish was ruled out by the linesman’s flag.
Despite the let off, it was a composed start from the visitors who soon began to threaten in an attacking sense.
Having taken 10 minutes to get his first touch of the game, Francois Zoko grew in influence as his impressive dribble 20 yards from goal ended with Tom Eaves seeing an effort from the angle saved by the legs of Benji Buchel.
The Glovers didn’t take long to take the lead however, going 1-0 up after just 14 minutes.
Charlie Clough’s under-hit back pass was perfectly read by Whitfield, with Buchel’s scrambled attempted clearance cannoning off the winger and floating into the back of the net.
The opener saw the Somerset outfit grow in confidence, stroking the ball across the park nicely as they looked to build on their goal advantage.
That plan was almost scuppered just past the 20-minute mark when Watson had a shot from range pushed behind by Artur Krysiak, before Town went close again at the other end.
More impressive hold-up play from Zoko saw the ball teed up for Dawson, with the Irishman’s dipping effort falling inches wide.
At danger of being overrun by Way’s side, Barnet boss Kevin Nugent switched to a 3-5-2 formation midway through the first half and almost immediately enjoyed a spell of pressure.
After a succession of corners, Barnet drew level on 30 minutes when Watson’s corner found its way into the back of the net via Nelson and, potentially, an unfortunate Glover.
Now level, the Bees kept Yeovil pinned in their own half and drew a good save from Krysiak when Akinde’s venomous effort was well parried.
Town managed to half the hosts’ momentum in the closing stages of the half, heading into the break with the game still in the balance.
Neither side made a change at the break and the stalemate remained as the game ebbed and flowed in terms of spells of pressure.
Barnet felt aggrieved not to have a penalty when David Tutonda went down inside the box, but despite strong appeals from the home terrace referee Stephen Martin waved play on.
Persisting with 4-4-2, Yeovil looked to take the lead for a second time and almost did so on the hour-mark after patient build-up play.
Having stroked the ball side-to-side, Whitfield penetrated the Bees with a neat run before teeing up Dawson on the edge of the box, with the fans’ favourite driving a shot just wide with Buchel beaten.
Moments later, Whitfield skilfully engineered space wide on the left before seeing his cross-cum-shot tipped over for a corner.
With fatigue beginning to set in for both sides, Way looked to reinvigorate his frontline by introducing Shayon Harrison for Eaves with a little over 10 minutes remaining.
Disrupted by a serious injury to Barnet’s Akinola, the game seemed to be ticking towards a draw with neither keeper seriously threatened before a fortuitous moment for the hosts.
Watson’s free kick from almost the halfway line drifted into the box and somehow nestled in the bottom corner with a flurry of players in the middle somehow unable to apply a touch.
If Yeovil were feeling unlucky they didn’t feel sorry for themselves, as they levelled the scores as the game ticked into stoppage time.
Shephard, impressive as an attacking outlet throughout the match, started a neat move before carrying his run on into the box where he was perfectly placed to turn Whitfield’s low cross into the net for his first senior goal.
The Glovers ended the match on the ascendency and looked for a winner only to be beaten by the clock, instead settling for a share of the spoils in the capital to round off a successful spell on the road.
Barnet: Buchel; Clough, Nelson, Dembele, Tutonda (Johnson 87’); Vilhete, Champion, Watson, Campbell-Ryce (Amaluzor 70’); Akinola (Coulson 85’), Akinde.
Subs not used: McKenzie-Lyle, Bover, Taylor, Cojocarel.
Yeovil Town: Krysiak; Shephard, Mugabi, Lacey, Dickson; Dawson, Butcher, Dolan, Whitfield; Eaves (Harrison 78’), Zoko.
Subs not used: Maddison, James, Bassett, Goodship, Jones, Sowunmi.