First-half strikes from Jason Roberts, Mikele Leigertwood, Noel Hunt and an own goal from Laurent Koscielny had earlier given the rampant Royals a lead which looked unassailable but a double from Walcott - along with efforts from Olivier Giroud and Koscielny in the right end – forced the match to extra time.
Marouane Chamakh edged the Gunners in front but substitute Pavel Pogrebnyak's header looked to have sent the game hurtling towards penalties before Walcott and Chamakh struck again to seal the win.
The astounding result gives Arsene Wenger a timely and unlikely boost after the club's stormy annual general meeting, while his opposite number Brian McDermott now faces a stiff challenge to pick his dejected players up in time for Sunday's relegation crunch clash against QPR.
In front of a raucous home crowd, Reading started the brighter and, in the second minute, Sean Morrison met Nicky Shorey's cross with a firm header which struck the post.
Less than 10 minutes later, they did take the lead, however, when Roberts met Hal Robson-Kanu's precise centre to sweep home from close range.
There was no discernible reaction from Arsenal and, on 18 minutes, the hosts doubled their advantage when Chris Gunter's cross cannoned off Koscielny and beat Martinez at his near post.
Wenger's makeshift team looked lost and, three minutes later, they were three down when Leigertwood drove to the edge of the box and unleashed a fierce effort which Martinez could only help into his own net.
Reading looked nothing like the side who have yet to record a Premier League victory this season and Hunt nodded in a fourth from another cross, this time from Garath McCleary, with 37 minutes gone.
|CHAMAKH IT SO
|FROM OUR LIVE COMMENTARY
Arsenal have sealed it! The ball is bouncing around all over the place and there is Chamakh to lob the ball over Federici, who is off his line, to seal the victory. 7-5, what a game this has been!
But Reading began the second half as they had ended the first and, moments after Leigertwood had tested Martinez again, the former Crystal Palace man raided down the left and clipped in in a cross which Ignasi Miquel directed narrowly over his own crossbar.
The Arsenal attack were at least starting to show signs of life, however, and after Leigertwood had spurned another decent chance, Walcott latched onto another Arshavin pass before hitting a left-footed effort which was kept out by a mixture of Federici and the post.
Just after the hour Wenger introduced German youngster Thomas Eisfeld and Giroud in place of Gnabry and Emmanuel Frimpong and the French striker took just seven minutes to make an impact, impressively heading in Walcott's corner.
Reading began to sense a first ever victory over Arsenal as the clock ran down but the Gunners had other ideas.
Koscielny's 90th-minute header set up a frantic finale, before Walcott's angled shot crossed the line despite Shorey's best attempts to clear. Carl Jenkinson followed up and smashed in to remove any doubt that this remarkable match was headed for extra time.
Two minutes in, the hosts almost retook the lead, McCleary surging through the centre of the pitch before jinking past two Arsenal defenders and forcing Martinez into a decent save low to his left.
But the momentum was now firmly with the Gunners and, two minutes before the interval, some good work from Giroud and Arshavin found Chamakh on the edge of the box and the much-maligned Moroccan fired a low shot through the legs of Kaspar Gorkss and past Federici.
Deflated but not yet defeated, Reading poured forward in the second period and Martinez had to save superbly with his legs to deny a goal-bound Morrison header. The Royals kept coming and they got their reward, as Gunter's shot was deflected into the path of the newly introduced Pogrebnyak, who powered a header in. The game was level with four minutes to go before penalties.
Play flowed from end to end, with both sides desperately searching for a winner, and Arsenal made the breakthrough when Arshavin's shot was hacked off the line by Gorkss, only for Walcott to hammer home the rebound.
Reading were in no mood to give up but their fate was sealed with seconds remaining when Chamakh latched onto a clearance and lobbed the despairing Federici to give a truly astonishing match the finish it deserved.