Royals striker Dave Kitson bundled home an injury-time corner as Coppell's men fought back from a disastrous first half during which a Steve Sidwell own goal after 18 minutes and a strike from Scottish international striker Stevie Crawford gave Argyle a 2-0 interval lead.
However, another own goal, from Graham Coughlan, brought a changed Reading into the game in the second half before Kitson struck in the second minute of added time.
A relieved Coppell conceded that runaway leaders Wigan looked likely Championship champions but added: "I would say, outside of them, there's another 16 teams with nothing between them.
From the off, Argyle were a continual menace to a Reading side that looked nothing like a side with Premiership pretensions, and the game was initially as one-sided a contest as is possible to imagine.
It was a minor miracle that the Royals reached the 18th minute before conceding, and, even then, they gave the Pilgrims a helping hand when Sidwell inadvertently deflected Mickey Evans' header past erratic goalkeeper Marcus Hahnemann.
A rare Reading attack ended with Argyle's French goalkeeper Romain Larrieu acrobatically turning aside Kitson's header, before Crawford picked up the scraps of Evans' challenge on Hahnemann to slide home the second.
Reading were a different prospect at the start of the second half, and Bobby Convey wasted a good chance to level before Coughlan stooped to head turned Nicky Shorey's free-kick past Larrieu.
Argyle soon regained the ascendancy, however, and Evans was unlucky not to score when his low shot hit the inside of a post.