The defending champions secured their place in the hat for the upcoming draw, after overcoming a stubborn Newcastle side at the Emirates Stadium in London.
The in-form Smith Rowe - a second-half substitute who had a red card overturned by VAR - opened the scoring for the Gunners in extra-time and Aubameyang put the tie beyond doubt when he added the second.
Arsenal boss Mikel Arteta told the BBC: "It was very impressive from Emile Smith Rowe because is playing with a lot of personality, a lot of risk. He is playing in areas where he needs to make things happen and he has got the talent to do it."
The win also sees Arsenal continue their recent run of good form.
Arteta said: "We want to keep going and win more games. It's always important to stay in the competitions. We want to fight for this competition again, so today was a big game for us."
Newcastle, on the other hand, will be frustrated by their early exit - especially after Andy Carroll missed two golden chances in normal time.
Steve Bruce, the Magpies' boss, felt like his side could've won the cup tie had they been more clinical in front of goal.
Speaking shortly after the full-time whistle, Bruce said: "You have to take your chances when they come along. We had the opportunity in the final few minutes and didn't grasp it. As a cup tie, it could have gone either way and we rue the missed chances.
"I thought Andy did fantastically well. If he had topped it off by scoring a goal, it would have been good for him. There were a lot of pleasing things."