The Royals, who have lost just once at home in the league all season, failed to make their superior possession count in the Argyle penalty area.
But Plymouth deserved credit for a terrific display of strength from their defence which came under constant pressure for the Royals.
The visitors though were lucky not to go behind after just 50 seconds when Steven Sidwell fired inches wide from 30 yards with keeper Luke McCormick, poleaxed by a Les Ferdinand challenge.
Nevertheless, Albion's counter-attacking style led to a couple of excellent openings with Graham Coughlan volleying wide in the 18th minute.
Ferdinand's header was then expertly saved by McCormick at the other end and Glen Little fired wide from an excellent position midway through the first half.
Before Reading's pressure it was Plymouth who should have taken the lead in the 38 minute but the Southampton loan signing Dexter Blackstock somehow headed wide from Scott Taylor's cross on his Argyle debut.
Ferdiand went close again with a header at the start of the second half and in the 72nd minute McCormick made another brilliant stop to keeper out Nicky Shorey's thunderbolt that was creeping in at the near post.
Plymouth, without an away win since Wigan in November, nearly blew it when their defence switched off in the 87th minute, but Nicky Forster's lob crashed off the bar.