Goals by Paul Gallagher and Jamie Mackie were cancelled out by Alex Pearce and Jimmy Kebe in a thrilling encounter at the Theatre of Greens.
Both sides could make decent claims to deserve the three points.
Reading had two shots cleared from the line and saw another attempt to hit the bar, while Argyle will point to a debatable offside decision against substitute Rory Fallon when they were 2-1 ahead.
Gallagher opened up proceedings for the Pilgrims when his close-range volley flew over Reading custodian Adam Federici's line after 20 minutes.
The Blackburn Rovers striker, on-loan to the Pilgrims, has now struck five times in the past four games, during which Paul Sturrock's have remained unbeaten.
The Pilgrims were unable to maintain their advantage and the Royals equalised within two minutes.
Marek Matejovsky charged down the left wing before timing a well-placed cross on to the head of Pearce, who steered it into the home side's net.
The Royals were unfortunate on two occasions not to go into half-time with a second goal to their name.
A well-placed Gallagher header on the line denied Pearce a second and David Gary also had to make a last-gasp clearance to thwart Stephen Hunt.
Mackie restored the lead for Argyle on the hour-mark with a spectacular strike from 35 yards out.
The striker managed to out-run the Reading backline before lining up a well-positioned rocket past Federici's net, much to the delight of the 14,014 supporters in attendance.
Yet the Royals continued to press forward in search of a second.
They hit the bar through Kalifa Cisse before eventually getting it close to the end when Mali international Kebe slotted a shot between the legs of Romain Larrieu.