Palace could have drawn level on 27 minutes but Clint Hill's header from a Moses corner went wide and the home side then suffered a major blow as John went off injured following an aerial challenge with Larrieu.
Palace's misery was almost compounded in first-half stoppage time when Rory Fallon's header came close to doubling Plymouth's lead.
Sears had two good opportunities after the break, but his long shot was saved by Larrieu, and the keeper made another good stop in a one-on-one with the teenager.
Both keepers were on excellent form in the second period, with Julian Speroni acrobatically tipping a Fallon header round the post in the Eagles' goal.
And Palace's pressure finally paid off when Lee headed home after Moses found space on the left and sent over a fine cross.
Palace then had a late chance to take all three points, but Sears' strike was kept out by Larrieu.
Crystal Palace boss Neil Warnock:
"Stern's having an x-ray now but it looks like the elbow has dislocated, which is obviously unfortunate.
"But that's the way football is, you have to get on with it. Considering what went on, I thought the players were terrific.
"We created 20 chances and we had to work very hard not to win the game."
Plymouth manager Paul Sturrock: "We're not the finished article and there are two or three more to bring in and benefit the squad.
"I don't think we deserved to win the game, to be fair.
"We ended up defending too deep and paid the price for it. But it's still early in the season and I am pleased with the attitude and the team spirit."
90:00+3:33 The final whistle goes and the game is over.
90:00+2:05 Alan Lee is adjudged to have handled the ball. Romain Larrieu restarts play with the free kick.
90:00+1:25 Alan Lee is penalised for a handball. Marcel Seip restarts play with the free kick.
87:16 Corner taken by Darren Ambrose from the right by-line played to the near post. Outswinging corner taken from the right by-line
by Darren Ambrose, Alan Judge makes a clearance.
86:44 Freddie Sears has an effort at goal. Romain Larrieu makes a save.
84:13 Carl Fletcher fouled by Alassane N'Diaye, the ref awards a free kick. Alan Judge produces a shot on goal direct from the free
83:47 Foul by Shaun Derry on Karl Duguid, free kick awarded. Carl Fletcher restarts play with the free kick.
82:37 Jamie Mackie fouled by Nathanial Clyne, the ref awards a free kick. Alan Judge crosses the ball in from the free kick, free
kick awarded for a foul by Rory Fallon on Julian Speroni. Julian Speroni takes the direct free kick.
82:01 Marcel Seip takes a shot and went wide left of the target.
79:21 Unfair challenge on Alassane N'Diaye by Alan Judge results in a free kick. Direct free kick taken by Julian Speroni.
78:27 Marcel Seip takes the free kick.
78:27 Substitution Sean Scannell joins the action as a substitute, replacing Victor Moses.
78:27 The assistant referee signals for offside against Freddie Sears.
77:32 Corner from the left by-line taken by Alan Judge, save made by Julian Speroni.
77:09 Inswinging corner taken from the left by-line by Alan Judge, Alassane N'Diaye manages to make a clearance.
70:43 Substitution Luke Summerfield leaves the field to be replaced by Alan Judge.
66:26 The referee blows for offside. Free kick taken by Romain Larrieu.
65:18 Substitution Karl Duguid on for Steven MacLean.
64:41 Shot from just outside the box by Shaun Derry goes over the crossbar.
62:42 Assist on the goal came from Victor Moses.
62:42 GOAL - Alan Lee:Crystal Palace 1 - 1 Plymouth Alan Lee finds the net with a headed goal from inside the penalty box. Crystal Palace 1-1 Plymouth.
62:38 The ball is delivered by Victor Moses,
59:20 Substitution Darren Ambrose on for Neil Danns.
59:20 Corner from the right by-line taken by Victor Moses, Header from close range by Clint Hill clears the bar.
56:41 Free kick awarded for an unfair challenge on Neil Danns by Rory Fallon. Free kick crossed by Clint Hill. Freddie Sears has
an effort at goal from the edge of the area that misses to the right of the target.
55:59 Steven MacLean is caught offside. Julian Speroni takes the free kick.
55:02 Free kick awarded for an unfair challenge on Nathanial Clyne by Steven MacLean. Direct free kick taken by Shaun Derry.
54:05 Clint Hill takes the free kick.
54:05 Booking The referee books Luke Summerfield for unsporting behaviour.
53:50 Luke Summerfield gives away a free kick for an unfair challenge on Victor Moses.
Correction - 53:11 Rory Fallon takes a shot. Save made by Julian Speroni. Outswinging corner taken from the right by-line by James Paterson,
save made by Julian Speroni.
53:11 Rory Fallon takes a shot. Save by Julian Speroni. Inswinging corner taken from the right by-line by James Paterson, save made
by Julian Speroni.
51:32 The referee blows for offside against James Paterson. Indirect free kick taken by Matthew Lawrence.
49:06 Effort from the edge of the penalty box by Freddie Sears goes wide of the right-hand upright.
46:51 Freddie Sears takes a shot. Jamie Mackie gets a block in. Corner taken by Victor Moses from the right by-line.
45:01 The second half kicks off.
45:00+5:17 The ref blows to signal half-time.
45:00+2:42 Rory Fallon takes a shot. Save made by Julian Speroni. Corner taken by James Paterson, Patrick McCarthy manages to make a
45:00+1:05 The official flags Victor Moses offside. Free kick taken by Romain Larrieu.
42:25 Freddie Sears takes a shot. Save made by Romain Larrieu. Corner taken right-footed by Victor Moses, Carl Fletcher makes a
41:07 Free kick awarded for an unfair challenge on Victor Moses by David McNamee. The ball is sent over by Clint Hill, Shot by Neil
Danns from deep inside the penalty area misses to the right of the target.
38:53 Neil Danns gives away a free kick for an unfair challenge on James Paterson. Free kick taken by James Paterson. The offside
flag is raised against David McNamee. Julian Speroni takes the indirect free kick.
30:26 Romain Larrieu takes the free kick.
30:26 Substitution Stern John leaves the field to be replaced by Alan Lee.
30:26 Stern John concedes a free kick for a foul on Romain Larrieu.
Correction - 26:52 Victor Moses delivers the ball from the free kick right-footed from left channel, clearance by Jamie Mackie. Corner taken
right-footed by Victor Moses, Close range headed effort by Clint Hill goes wide of the left-hand upright.
26:52 Free kick crossed by Victor Moses, clearance by Jamie Mackie. Corner taken by Victor Moses, Clint Hill produces a header from
close range which goes wide of the left-hand upright.
26:52 Booking Krisztian Timar goes into the referee's book.
Correction - 26:42 Free kick awarded for an unfair challenge on Victor Moses by Krisztian Timar.
26:42 Victor Moses fouled by Krisztian Timar, the ref awards a free kick.
25:10 Carl Fletcher challenges Alassane N'Diaye unfairly and gives away a free kick. Julian Speroni takes the free kick.
21:43 Free kick awarded for an unfair challenge on Freddie Sears by Krisztian Timar. The free kick is delivered right-footed by
Neil Danns from left channel, Jamie Mackie makes a clearance.
19:59 Free kick awarded for an unfair challenge on Stern John by Krisztian Timar. Strike comes in from Victor Moses from the free
19:20 Jamie Mackie produces a left-footed shot from just outside the box that misses to the right of the net.
Correction - 17:54 The referee blows for offside against Stern John. Romain Larrieu takes the indirect free kick.
17:54 Freddie Sears is ruled offside. Free kick taken by Romain Larrieu.
14:34 Unfair challenge on Victor Moses by David McNamee results in a free kick. The ball is crossed by Neil Danns, Header from close
range by Patrick McCarthy misses to the right of the target.
13:47 Steven MacLean takes a shot. Save made by Julian Speroni.
13:03 Effort from the edge of the box by Freddie Sears goes wide of the left-hand upright.
10:02 Shot from 35 yards by James Paterson went wide of the left-hand upright.
6:51 Effort from 12 yards by Neil Danns. Save by Romain Larrieu.
5:33 Stern John takes the outswinging corner, save by Romain Larrieu. Stern John has an effort at goal from outside the penalty
box missing to the wide right of the goal.
4:28 Luke Summerfield provided the assist for the goal.
4:28 GOAL - Krisztian Timar:Crystal Palace 0 - 1 Plymouth Krisztian Timar finds the back of the net with a goal from inside the six-yard box high into the middle of the goal. Crystal
Palace 0-1 Plymouth.
3:47 Matthew Lawrence gives away a free kick for an unfair challenge on Gary Sawyer. The free kick is delivered right-footed by
Gary Sawyer from right channel, Clint Hill manages to make a clearance. Corner taken left-footed by Luke Summerfield from
the right by-line,
2:37 Alassane N'Diaye sends in a cross, Headed effort from close range by Stern John goes wide left of the goal. Jamie Mackie is
ruled offside. Julian Speroni restarts play with the free kick.
0:00 The referee gets the game started.
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