A youthful Gunners set-up endured a nightmare start, going three down after 20 minutes and four down after 37 as their defence imploded.
Theo Walcott gave the visitors hope at the interval with his first before Olivier Giroud, Laurent Koscielny and Walcott's second forced extra-time in the final half hour of regulation time.
Marouane Chamakh put the visitors ahead for the first time in the additional 30 minutes only for substitute Pavel Pogrebnyak to restore parity at 5-5.
But Walcott hammered home a loose ball to ensure possession of the match ball before Chamakh ensured there would be no more surreal drama on the counter-attack right at the end.
Reading came into the home cup tie in search of their first win over Arsenal after nine failed attempts, and halfway through the first 45 minutes it looked almost certain to finally happen.
Testing their guests early on when Sean Morrison's header from a corner was cleared off the line by Emmanuel Frimpong and Jay Tabb's close range strike was parried by 20-year-old Argentine goalkeeper Damian Martinez, Noel Hunt then crossed beautifully for strike partner Jason Roberts to volley the opener into the roof of the net after 12 played.
The away side showed no immediate signs of learning from their complacency and eight minutes later, the lead was doubled when the Royals had all the space in the world to move forward once more, with Koscielny putting a cross from the right into his own net.
And it took the hosts a further two minutes to add a third when static defending led to a corner pinballing off several red shirts until Mikele Leigertwood took the initiative to advance into the area and lash in a drive which the inexperienced Martinez really should have stopped.
When the Arsenal midfield surrendered possession with little fight on 37 minutes, allowing Garath McCleary to pick out the head of Hunt with a lovely delivery for 4-0, it appeared that one of Arsene Wenger's more embarrassing days on the job was on the horizon.
But the Londoners showed signs of improvement in every area for the final moments of the half, and when Walcott latched onto Andrei Arshavin's neat through pass before lifting the ball over the onrushing Adam Federici, Wenger's half-time team talk had an angle after all.
Arsenal came out for the second half the more determined side but despite controlling the majority of play, it wasn't until the introduction of Giroud that things began to really happen for them.
Making an instant impact seconds after his arrival, the French forward cleverly glanced in a corner with his head to halve the deficit with 25 minutes left before another flag kick on 89 minutes saw Koscielny gain redemption for the own goal and make it 4-3.
And as stoppage time arrived, Walcott fired Giroud's flick-on towards goal and though his effort appeared certain to cross the Reading goal line, Carl Jenkinson made absolute sure by burying the follow-up of what nonetheless shouuld stand as Walcott's second.
The Gunners kept their momentum sweeping into extra-time and with three minutes remaining of the first 15-minute period, Chamakh created space for himself just outside the box to hammer a low 20-yarder into the near bottom corner and put his side ahead for the first time.
Any assumptions that Reading had completely given up after throwing away the four-goal lead were answered five minutes before potential penalties as Pogrebnyak put the finishing touches on Chris Gunter's initial half-volley.
But before Wenger or Brian McDermott could begin to jot down their first five spot kick takers, Arsenal bombed forward in search of one more chapter to a crazy story which came in the 120th minute as Walcott smashed home a loose ball in the Royals box for his hat-trick.
And with the hosts going all-out in search of another twist in the fourth and final injury time period of the match, Chamakh remained forward to receive a long clearance, lobbing the out-of-position Federici for Arsenal's seventh.