Peter Hartley volleyed the visitors ahead in first half stoppage time, before Jake Jervis bagged a second half brace either side of Lloyd James' 82nd minute penalty.
Orient named an unchanged side for their second successive home game, with the inclusion of Sammy Moore on the bench being the only change to the squad which defeated Dagenham & Redbridge.
Saturday saw the O’s got off to a perfect start by grabbing an early lead against Dagenham, and it was almost an identical beginning for the hosts as Jay Simpson saw a shot deflected behind for a corner.
The positive opening few minutes then saw Simpson come close again, as a Lloyd James free-kick evaded the head of Armand Gnanduillet before dropping just behind the 27-year-old as he looked to bundle home a fourth minute opener.
Plymouth started to grow into the game and on the 10th minute Graham Carey looked to beat O’s goalkeeper Alex Cisak, but his shot was comfortably saved by the Aussie.
A good piece of defending from Nicky Hunt ensured the game remained goalless moments later, when the former Bolton man got a vital touch on Jamille Matt’s pull back which had Reuben Reid waiting to slot home from six yards.
Both sides were battling well in the middle of the park as chances became few and far between, though midway through the first half Pilgrims captain Curtis Nelson volleyed a Carey free-kick narrowly over the bar.
Carey’s delivery from set pieces was proving the biggest threat for the visitors and soon after the winger curled an effort from 25 yards just wide of Cisak’s near post
With the half drawing to a close Orient were able to create a couple of half chances on the 42nd minute as Hunt’s marauding run into the box resulted in a shot being blocked, before Nigel Atangana also saw an attempt repelled by the Pilgrims defence.
It looked as though the sides would be going into the break level, but with the match in the second minute of stoppage time Peter Hartley volleyed Argyle ahead after getting on the end of Carey’s free-kick, who appeared to go down softly under the challenge of Hunt.
Having suffered the late blow of conceding just before the interval, Orient returned for the second half unchanged though struggled to create any chances until Gnanduillet directed a header from a James corner straight at Luke McCormick shy of the hour.
Cisak was then called into his first save of the half moments later, parrying Carey’s strong fierce down into the ground before holding.
With 62 minutes played Orient made their first change of the evening as Ollie Palmer was introduced in place of Gnanduillet.
Within two minutes of his introduction the forward had a hand in an O’s attack to release Blair Turgott down the left, who then went down inside the box after tangling with Kelvin Mellor only to be shown a yellow card for simulation.
Knowing a win was needed to keep any Play-Off hopes alive, Orient continued to try and find a way beyond a resolute Plymouth defence and made their second substitution with 20 minutes remaining as Scott Kashket replaced Clohessy.
However, any chance of an O’s comeback was made even harder on the 78th minute however when Plymouth doubled their lead. Carey was once again the provider, whipping a free-kick in from the right for substitute Jake Jervis to head beyond Cisak.
Refusing to give up on the game, Orient were then handed a way back eight minutes from time when awarded a penalty after Palmer had been bundled over by Jordan Forster, who was subsequently booked for the challenge.
James stepped up to take the spot-kick and was able to set up a tense final period by going low to his right and sending McCormick the wrong way.
Calaum Jahraldo-Martin was then thrown on for the final minutes in place of Turgott, but with the match in the second minute of stoppage time Plymouth put the game to bed when Jervis drilled home his second of the night after Matt had raced onto Mathieu Baudry's soft header back towards goal.
The defeat leaves Orient five points off 7th placed AFC Wimbledon with three games of the season left to play.
ORIENT: Cisak, Hunt, Baudry (C), Brisley, Binnom-Williams, Clohessy (Kashket 70), James, Atangana, Turgott (Jahraldo-Martin 86), Gnanduillet (Palmer 62), Simpson
SUBS: Sargeant, Ramage, Payne, Moore
GOALS: James (82 pen)
BOOKED: Turgott (64)
PLYMOUTH: McCormick, Mellor, Nelson (C), McHugh (Forster 55), Purrington, Houghton, Hartley, Boateng, Carey, Matt (Wylde 90+5), Reid (Jervis 37)
SUBS: Dorel, Sawyer, Harvey, Tanner
GOALS: Hartley (45+2), Jervis (78 & 90+2)
BOOKED: Boateng (62), Forster (82)
REFEREE: Kevin Johnson (Ian Cooper HT)
ATTENDANCE: 4,908 (1,037)