Having finished 1-1 after 90 minutes, Bruno Guimaraes saw his spot kick saved by Jay Lynch before Fleetwood's teenage defender Conor Haughey lashed home an emphatic penalty to spark a pitch invasion at Highbury Stadium as the hosts triumphed in one of the competition's greatest upsets.
"The biggest night in the club's history in terms of opposition coming to town and we've managed to beat the (Premier League) champions," Fleetwood manager Matt Lawlor said.
A drone hovering above the stadium caused an eight-minute delay soon after the match kicked off on Tuesday night (Wednesday AEDT).
Fleetwood, 18th in League Two, dared to dream after Fulham loanee Aaron Loupalo-Bi put them in front after 21 minutes against a much-changed Arsenal side struggling to find any fluidity.
The halftime introduction of Martin Odegaard changed the game as the Gunners looked much improved after the break, drawing level in the 50th minute when Viktor Gyokeres managed to net his first goal of the season.
But as Arsenal turned up the the heat without reward, their frustration boiled over as their teenage prodigy Max Dowman was sent off with five minutes left to play.
There was still time for Lynch to make huge saves from Ben White and Odegaard before it went to a shootout in which Fleetwood were perfect from the spot to secure a historic 5-3 win.
"We took heart from Grimsby beating Man United last year," Lynch said.
"Amazing for the club, the town. Honestly it means everything to everyone."
Gunners boss Mikel Arteta lamented: "A really sad day for us.
"Congratulations to Fleetwood. I have nothing to fault the players (for) in terms of their attitude, application, the intensity they put in throughout the game.
"But when you are that superior ... and you generate so many situations, actions, volume of shots and chances, you have to score three, four, five, and capitalise on that.
Bradford City are through to the last eight for the first time since they reached Wembley in 2013, scoring a 2-0 win over Peterborough United in an all-League One affair at Valley Parade.
Bradford manager Michael Duff had called for his side to be more productive from corners and they obliged on 13 minutes when Callum Connolly's set-piece was turned in by defender Macaulay Gillesphey.
Peterborough goalkeeper Alex Bass made a number of saves before the break, but after twice going close to scoring they conceded again in the 67th minute through Adam Phillips, who also had another cleared off the line.
With The AP.
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