In a game short of major clear cut chances, both sides will be happy with a share of the spoils in the season curtain raiser.
The visitors took an early lead in the fifth minute, Krisztian Timar smashing home Luke Summerfield's corner after some poor Palace defending.
Argyle's dream start jolted Palace into action, Victor Moses missed a glorious chance from six yards out to put the home side level, before Stern John's cheeky back heel was ruled out for offside.
John's afternoon came to a premature end just 38 minutes into his Eagles debut after he was stretchered off with a dislocated elbow falling awkwardly in the box.
Freddie Sears and Neil Danns both missed chances for Palace to equalise before the break, but the south Londoners could easily have fell two behind after Jim Paterson and Rory Fallon were thwarted by keeper Julian Speroni.
Steven MacLean should have doubled Argyle's lead in the 53rd minute, but he sent his free header from Jamie Mackie's cross straight at Speroni.
And the Pilgrims midfielder was made to pay for his miss in the 62nd minute when Lee secured a point for Palace - thumping a header from Moses cross past Romain Larrieu.
Alan Judge went close with a 25-yard free-kick in the final five minutes before Sears missed a gilt-edged chance in the 88th minute as it ended all-square.