Theo Walcott was the hero, claiming a 95th-minute equaliser to force extra time and then slamming home the decisive goal in the last minute of the extra period to complete 120 unforgettable minutes of football.
"There were so many turning points," said Arsenal coach Arsene Wenger.
"You cannot play for Arsenal and give up. The players understood that at half-time. Give them credit -- they responded very well.
"The first set is for us, it was a tennis game today."
The win enabled the Gunners to take their place in the last eight for the 10th successive season, but Reading coach Brian McDermott -- a former Arsenal player -- was left to wonder how victory had eluded his side.
"It was suicide what went on in the second half and extra time," he said.
"You play each game on its merits but it was extraordinary. I've never seen anything like it. We have to dig deep and move onto the next game versus QPR."
Wenger made 11 changes to the Arsenal team that beat Queens Park Rangers 1-0 on Saturday and Reading tore into them from the off, with Sean Morrison heading against the post after two minutes.
The onslaught did not let up, and the hosts were 3-0 up after 20 minutes through a Jason Roberts volley, a Laurent Koscielny own goal, and a howler from Arsenal goalkeeper Damian Martinez that allowed Mikele Leigertwood to score.
Noel Hunt's header made it 4-0, before Walcott dinked the ball over Reading goalkeeper Adam Federici to pull a goal back for Arsenal in first-half injury time.
It looked destined to be a mere consolation, but goals from substitute Olivier Giroud and Koscielny -- at the right end -- gave Arsenal hope.
Walcott squeezed a shot over the line in the 95th minute to take the game to extra time, with Carl Jenkinson following up to make sure.
Reading's players were angry that more than the allotted four minutes of injury time had been played, and they were given further reason to curse their luck when Marouane Chamakh drove home to put Arsenal ahead in the 103rd minute.
Unbelievably, there was more drama to come.
Pavel Pogrebnyak headed in to make it 5-5 with five minutes to play but with penalties looming, Walcott slammed home to restore Arsenal's lead before Chamakh lobbed Federici to complete a remarkable evening of sport.
Although Reading fell short in the most agonising fashion, there were upsets elsewhere on Tuesday.
Second-tier Leeds United followed up their victory over Everton in round three to beat Premier League Southampton 3-0 and reach the last eight for the first time since 1996.
Middlesbrough, of the Championship, won 1-0 at top-tier neighbours Sunderland, while Bradford City of third-tier League Two overcame top-flight Wigan Athletic 4-2 on penalties after a 0-0 draw over 90 minutes.
There was no fairytale for League One Swindon Town, however.
The former Premier League club, managed by Paolo Di Canio, fought back from 2-0 down to level with Premier League Aston Villa, only for Belgian striker Christian Benteke to hit a 90th-minute winner for the visitors.
Wednesday's stand-out tie sees Manchester United return to Chelsea three days after the stormy Premier League clash between the teams that culminated in accusations that referee Mark Clattenburg verbally abused Chelsea's players.
Liverpool coach Brendan Rodgers is set for his first meeting with Swansea City since leaving the South Wales club in the summer, while Norwich City host Tottenham Hotspur in another all-Premier League tie at Carrow Road.