Braces from Yakou Meite and Josh Barrett sent Reading through to the third round of the EFL Cup having twice been behind in the cup tie.
Plymouth twice took the lead but were pegged back as Barrett equalised on two occasions, scoring a spectacular second goal.
Meite won a penalty and converted the spot-kick with a few minutes left and then added a fourth Royals goal in stoppage time as the visitors hit Plymouth on the counter attack.
Plymouth started the brighter of the two sides as McFadzean whipped a cross in the air for Taylor who forced goalkeeper Sam Walker to tip the ball over the crossbar.
Reading then created their first opportunity of the match just moments later as Yakou Meite stole possession in the box and hit a shot from a tight angle to force Cooper into making a smart save.
The hosts continued to create the better chances as Mayor pulled the ball back for Baxter inside the box but the striker wasted his chance as he ballooned the ball over the bar.
Akinwale Odimayo then had to come to Reading’s rescue to turn a Plymouth cross away for a corner with several Plymouth players ready to pounce on the loose ball.
Plymouth broke the deadlock in controversial style as a goalmouth scramble saw Rudden claw the ball back into play after it had gone behind the line and Ryan Taylor converted a scrappy finish.
The referee awarded the goal after speaking to the linesman on the nearest side to confer whether the ball had gone out of play, however the replays showed that the referee had made an obvious error.
The goal seemingly kickstarted the Royals into life as Meite hit a low drive which was spilled by Cooper who recovered the ball just as Josh Barrett was arriving for the follow up.
With 35 minutes gone, Reading levelled the tie against their League Two opposition. Charlie Adam caressed a through ball out to the wing to find Barrett who cut inside into the box and fired a low effort into the far corner.
With a surge in confidence having found the equaliser, Barrett went close again as he picked the ball up 20 yards from goal and curled an effort just wide of the far post.
Argyle retook the lead 10 minutes after the break as Jose Baxter struck a shot from 25 yards into the bottom corner to beat Walker. Reading were again unhappy at the referee after a supposed foul on Michael Olise in the build up to the goal, but their protests fell on deaf ears as they fell behind for the second time in the match.
Having just come on as a substitute, Sam Baldock came close to levelling the game after Meite fed him the ball but his goalward shot was hooked off the line.
Barrett then put Reading back on terms for the second time in the tie with a stunning curling effort. He cut inside from the flank onto his right foot and finessed the ball beautifully into the top right hand corner.
Reading were then awarded a penalty with just three minutes remaining in the contest after Meite burst into the box and was fouled by the keeper.
Having missed a spot-kick against Cardiff City in the league, Meite made no mistake this time as he sent the keeper the wrong way to put the Royals in front for the first time in the contest.
Reading then broke on the counter attack and Baldock unselfishly switched the ball to Meite who squeezed a finish past the keeper to add his second of the game and to put Reading’s name into the third round draw.
Reading: Walker, Rinomhota, Obita, Loader, Meite,
Olise, Howe, Adam, Osho, Odimayo, Barrett
Subs: Virginia, Morrison, Baldock, Boye, Medford-Smith, Nevers, Coleman
Plymouth Argyle: Cooper, Grant, Canavan, Wooton, Moore, McFadzean, Mayor, Edwards, Baxter, Rudden, Taylor.
Subs: Sawyer, Aimson, Grant, Lolos, Randel, Palmer, Fletcher.
