Town dominated the game but couldn't carve out many clear-cut chances, and Ollie Palmer's fierce strike on the edge of the box with just three minutes left gave Artur Krysiak no chance as Orient went back to London with the win.
Darren Way made just one change for the final game of the League Two season, as Leroy Lita was replaced in the starting eleven by Harry Cornick, after the Bournemouth loanee came off the bench to score the late winner in last week’s 4-3 victory away at Barnet.
Yeovil started the game brightly and it was the Glovers who had the first chance of the afternoon after just five minutes. Francois Zoko made space on the edge of the penalty area, and his powerful right-footed shot flew just over debutant Sam Sargeant's crossbar for a goal-kick.
Nathan Smith nearly opened the scoring himself two minutes later, just a week after scoring his first goal for seven years in the turnaround at Barnet last week. Matty Dolan's whipped corner found the centre-back free in the box, but his bullet-header went just wide of the Orient goal.
The game slowed down in tempo after that frantic opening ten minutes, but with a final few minutes of the half left, Sargeant had to be alert to stop Liam Shephard's low drive from 25 yards from going in, as the young stopper put the ball behind for a Town corner that came to nothing.
Orient nearly stole the lead on the stroke of half time, as the away side worked it well down the right hand side and a cross was put into the box towards their top scorer Jay Simpson, but the 25-goal man's attempted volley on the turn was foiled as he completely missed the ball and Yeovil cleared.
The second half started with Huish Park baked in the beautiful May sunshine, and Yeovil began the half brightly too. Liam Walsh's powerful shot was parried away by Sargeant, and Town were looking threatening after the interval.
Cornick nearly opened the scoring after a powerful run into the box, but his goal-bound shot was cleared away by Orient right-back Sean Clohessy, as Town looked to sign off their season in style.
Way made his first change of the afternoon as Marc Laird was replaced by Brandon Goodship, before being forced to make a second shortly after as Cornick limped off as Jack Compton came on in his place.
With just over ten minutes left, Town had their best chance to go in front. Walsh's whipped corner found Smith in space, but the centre back's left-footed shot from just inside the six yard box bounced into the ground and went over the bar into the Thatcher's Gold stand.
Way's final change of the afternoon saw Zoko taken off to be replaced by Omar Sowunmi, as the giant striker made his first game after a lengthy spell on the sidelines and was welcomed with a rapturous applause.
But with five minutes left, Orient took the lead. A clearance by Alex Lacey was intercepted by Palmer, and his powerful right footed shot from the edge of the box crashed past Krysiak onto the post and rolled into give the visitors the opener.
Compton very nearly equalised with seconds left but his header from Ryan Dickson's pinpoint cross went straight into the arms of Sargeant. Town put the visitors under late pressure, as Krysiak came up for a free-kick and a corner, but Orient held out for all three points.
Yeovil: Krysiak, Roberts, Lacey, Smith, Dickson- Shephard, Walsh, Dolan, Laird (Goodship 62’)- Cornick (Compton 66'), Zoko (Sowunmi 83').
Subs not used : Weale- Bird, Jeffers, Lita.
Orient: Sargeant- Hunt, Pollock (Koroma 56'), Brisley (Turgott, 21), Ramage- Clohessy, James, Moore, Semedo- Palmer, Simpson (McCallum 73').
Subs not used: Cisak, Kashket, Moncur, Judd.
Attendance: 4,613 (317 away)