After an opening 45 minutes largely devoid of opportunities, the hosts took the lead in first-half stoppage time courtesy of a close range Francois Zoko finish.
The Glovers went close on two occasions after the break before Orient levelled late on through Gavin Massey, to make it a frustrating afternoon for the Glovers.
Darren Way made five changes to the side that went out of the Checkatrade Trophy in midweek, when Town had eight players unavailable.
Artur Krysiak returned between the sticks, whilst Liam Shephard re-entered the fray after suspension on Tuesday night.
Captain Darren Ward – rested at Kenilworth Road – returned to partner Nathan Smith in the heart of the Glovers defence, with Alex Lawless making his first appearance in seven matches due to injury.
Having missed the trip to Luton due to ineligibility, Jean-Louis Akpa Akpro was the fifth and final change, starting in the front three.
Despite the numerous changes, Town started with nine of the 11 that featured at Hartlepool seven days previous and as in County Durham, the Glovers were slow to get going.
Conversely, the O’s were quick out of the blocks and tested Krysiak in the open few minutes when Nigel Atangana stung the hands of the Polish stopper with a powerful effort.
Unscathed from a shaky opening five minutes, the game plateaued into an even share of possession, with neither side engineering anything by way of a meaningful opportunity.
In fact, Yeovil had to wait until the 20th minute for their first flurry of pressure, with a succession of corners and a deflected Ben Whitfield strike stroking the side-netting.
However, it was from a Green and White corner that the London outfit spurned the best opportunity of the opening 45 minutes.
Having sprung a counter-attack, Sandro Semedo and Gavin Massey found themselves two on one against Liam Shephard, but the former ignored his strike partner and eventually was challenged by Town’s lone defender.
That spurned opportunity triggered Town into life, who produced two chances of their own in quick succession.
Neat build-up saw Whitfield slide a ball into Shephard, but in unchartered territory the full-back could only blaze into the side-netting.
Moments later, and just past the half-hour mark, Zoko curled an effort from range over the bar, as Town became more effective in the final third.
A lengthy delay for Krysiak who required treatment for a facial injury looked to have killed off any momentum, but Yeovil took the lead on the stroke of half-time.
Tom Eaves’ neat turn and deflected shot was well pushed away by Sam Sargeant in the visiting goal, but Zoko showed his guile to follow in and expertly find the back of the net, becoming Town’s top scorer with nine goals in the process.
After the break, and looking to avoid a seventh straight defeat, Orient kicked off the second half when Massey fired straight at Krysiak, before the hosts took control.
Enjoying the majority of the play, Way’s side produced a trio of chances as the game ticked past the hour mark.
After a spellbinding run from Zoko, the veteran teed up apprentice Whitfield, but the Bournemouth loanees strike was straight at Sargeant.
Looking to put the game to bed, Eaves flashed a low drive inches wide from the edge of the box before Akpa Akpro did the same from inside the box.
Orient used all three of their subs in a bid to turn the tide, and it resulted in a spell of pressure as the game ticked towards the final 10 minutes.
Danny Webb’s side committed numbers forward as Town slumped deeper, and with two minutes of normal time remaining the O’s levelled.
Paul McCullum’s effort only fell to Massey at the back post who fired into the roof of the net to ease Orient’s poor start to 2017.
With little time for either side to find a winner it ended with a share of the spoils at Huish Park, resulting in a frustrating afternoon for the hosts.
Yeovil Town: Krysiak; Shephard, Ward, Smith, Dickson (Mugabi 79’); Whitfield, Lawless, Dolan; Akpa Akpro (Harrison 71’), Eaves, Zoko (Sowunmi 90′).
Bookings: Lawless 55’, Dolan 78’
Subs not used: Maddison, James, Butcher, Goodship.
Leyton Orient: Sargeant; Judd, Erichot (Kennedy 45’), Parkes, Hunt; Atangana (Koroma 55’), Kelly, Collins; Massey, Liburd (McCullum 54’), Semedo.
Bookings: Semedo 71’, Collins 73’, Kelly 75’
Subs not used: Grainger, Mezague, Moncur, Dalby.