The Gunners were heading for a first defeat against lower-league opposition in this competition since 1983 after Josh Murphy fired the visitors into a first-half lead.
With five minutes of normal time left to play Eddie Nketiah came off the bench to score a leveller, before netting the only goal in the additional 30-minute period to win the tie for the Gunners.
Relive how the 90 minutes of action unfolded with Sports Mole's live text coverage below.
STARTING XI: Macey; Debuchy, Elneny, Holding; Nelson, Coquelin, Wilshere, Maitland-Niles; Walcott, Iwobi; Giroud
SUBS: Iliev, Osei-Tutu, Sheaf, Dasilva, Willock, Nketiah, Akpom
STARTING XI: Gunn; Pinto, Zimmermann, Klose, Husband; Reed, Trybull; Vrancic, Maddison, Murphy; Oliveira
SUBS: McGovern, Martin, Jerome, Hoolahan, Wildschut, Stiepermann, Franke
Arsene Wenger: "I always used this cup to give a chance to young boys. We went to the final with a very young team and nearly won it [in 2007 and 2011]. I always focus on winning trophies in the Premier League and FA Cup domestically, and always used the League Cup as an education for our young players. But with this team I have the squad to go further, so let's see. I will continue to rotate my squad. I've gone into that rotation policy and afterwards you have to continue to do it, especially when both teams work well and both teams support each other at the moment."
Daniel Farke: "There is no pressure on us because 19 times out of 20, Arsenal would go through to the next round. There is always that one time though - and that time is special. I like situations where people don't expect you to create special moments. We've won our last five away games and that gives us confidence. It is a big task, but I'm concentrated on bringing the best result back to Norwich City. We are full of respect for Arsenal, but we want to beat them. That's our topic and what we are trying to do - we are looking to create something special."
ARSENAL SUBS: Iliev, Osei-Tutu, Sheaf, Dasilva, Willock, Nketiah, Akpom
NORWICH CITY SUBS: McGovern, Martin, Jerome, Hoolahan, Wildschut, Stiepermann, Franke