In a high tempo opening 45 minutes, the green and whites produced a bright display whilst being backed by a raucous away following.
Remeao Hutton went closest to breaking the deadlock whilst at the other end Simeon Akinola rattled the crossbar with the virtually the last act of the half.
The Barnet striker went close again soon after the restart only to be denied by an in-form Stuart Nelson before finally converting from the penalty spot on 61 minutes in what proved to be the difference.
Starting a new era in the capital under the tenure of Darren Sarll, the Glovers boss handed out eight debuts after a busy summer of recruitment.
A new back three of Albi Skendi, Lee Collins and Tom Bradbury sat in front of the familiar face of Nelson, whilst Hutton, Tom Whelan, Lawson D’Ath, Rhys Murphy and Myles Hippolyte completed the fresh faces.
Remaining from last season, Craig Alcock and Matt Worthington finalised the starting XI with Luke Wilkinson and Carl Dickinson the only injury absentees.
On a humid afternoon at The Hive, Sarll’s side had the Bees in a sweat early on with Hutton close to a debut to remember.
With Town’s high press winning possession in the Barnet half D’Ath had a shot blocked inside the box before the Birmingham loanee – who only joined on Friday – demonstrated a neat turn before forcing Scott Loach to parry his strike away.
Retaining the sharpness they demonstrated in pre-season, the visitors continued to threaten in the opening quarter-of-an-hour with their high tempo approach paying dividends.
Having notched six goals in as many games in July’s friendlies, Murphy looked the most likely again on his competitive debut as he forced an acrobatic save from Barnet’s keeper with a shot from the edge of the box.
As the one-way traffic continued, Hippolyte drilled a shot that called the Bees’ stopper into action again before Darren Currie’s side enjoyed a good spell of pressure themselves.
Gaining some momentum from the wings, the hosts went close twice in quick succession.
Firstly, Nelson had to be at his best to get a fingertip to Jack Taylor’s glancing header before Akinola headed just over the bar from six yards.
With both central strikers causing all the problems for both sides, it was Akinola who had the last act of the half when his looping strike from 18 yards came back off the bar to round off an entertaining and end-to-end start to the 2019/20 Vanarama National League campaign.
Maintaining the high intensity straight from the restart, Akinola was quick to try and finally open his tally for the season.
Dan Sparkes’ cross looked to have given the striker a tap in but for Nelson to spread himself and brilliantly block the volley from a matter of yards.
With Yeovil’s number one doing his job, the Glovers’ final line of defence was finally breached just past the hour mark.
After Collins tripped Akinola in the box to concede a penalty, the Barnet number 14 made no mistake from 12 yards to finally come out on top in his duel with Nelson.
Now with the lead, the Bees understandably took the sting out of the encounter as the green and whites struggled to enjoy the territory and pressure they did in the first half.
Unable to test Loach from open play as they did in the opening 45 minutes, the visitors almost drew level from a free-kick.
Lining up 25 yards out, Murphy looked to curl a strike into the bottom corner but was denied by a full-stretch home ‘keeper to maintain Barnet’s lead.
In a game only separated by a defensive mistake which resulted in a penalty, Skendi closed out the match as an additional striker in a final roll of the dice but a dramatic finish wasn’t to come as the Bees claimed all three points.
Barnet: Loach; Alexander, Santos, Reynolds, Tutonda; Dunne, H. Taylor, J. Taylor; Elito (Mason-Clark 85′), Akinola (Coulthirst 73′), Sparkes.
Subs not used: Matrevics, Adams, Barham.
Yeovil Town: Nelson; Skendi, Collins, Bradbury; Alcock, Whelan, D’Ath, Worthington, Hutton (Shako 80′); Murphy, Hippolyte (Seager 46′).
Bookings: Collins 60′, D’Ath 78′.
Subs not used: Driscoll, Ojo, McCoy.