In a chaotic match Galway's character and class was evident which pleased manager Pádraic Joyce.
Armagh's late comeback mission forced extra-time when Rian O'Neill nailed a pressure free, but the drama continued to unfold.
Seán Kelly's controversial sending off and Cillian McDaid's remarkable equaliser were other talking points at GAA headquarters.
"It was a thrilling game to be honest, it was a good footballing game," Galway boss Joyce reflected.
"Cagey at the start, seven points each at half-time, and then second half we opened up a good bit and got ahead near the end of the game and played some good football but then lost our way. It's something we’ll address because we did the same against Mayo and Roscommon and we addressed it and we still lost our way. We had the game won three or four times and Armagh came back.
"The scenes at full-time, they were ugly scenes. They shouldn’t be happening, but they happened at the same time. We lost our captain [Sean Kelly to a red card] in extra-time. I don’t understand how they pick out one player, but we’ll look at the video and see what happened there.
"We had to take control of the game in extra-time, which we did. We showed good character. Even then to get the sucker punch of a goal in the second half of extra-time. It looked like we were dead and buried but the lads showed brilliant heart, brilliant character and kept playing football, kept playing through the lines and Cillian popped up with an amazing equaliser at the end."
The resolve and resilience Galway demonstrated encouraged Joyce. "They did and they stuck at it," Joyce said.
"Coming in at full-time, it nearly felt like a loss. We were five or six up and lost it, (the officials ) found eight minutes injury-time and then found two more to play 10.
"It was what it was, but in fairness to the lads, they showed great character and great resilience. Galway have been accused of being soft in the past and at least they [showed they were going] in a good direction because Galway had to go and win a big game in Croke Park and that was a big game and a tough game. We’ll get ready for Derry now in 13 days' time."
In the penalty shootout Galway stayed ice cool as Shane Walsh, Damien Comer, Rob Finnerty, and Matthew Tierney converted under duress.
"We’ve been practicing penalties since last December, since we started training," Joyce remarked when asked about preparing for a shootout.
"Because we knew the way the game was going something was going to happen and in fairness to Shane [Walsh], Rob [Finnerty], Damien [Comer], Mattie Tierney – and Kieran Molloy would have been our fifth taker – they practice them nearly every night. They take penalties most nights."
Joyce acknowledged the rich contribution made by Billy Mannion in extra-time after Kelly's dismissal.
"Billy Mannion came in for us and he set up a brilliant goal. Great footballer, his Championship debut for Galway. What a place, what a time to do it. He had great composure to hand the ball across to Cillian for the goal.
"We knew that the game wasn’t lost at the same time. There were still 20 minutes to be played and while it felt like a loss at full-time, I think the lads regrouped well. We told the lads, ‘Go back to playing football’ and just worked the ball through the lines, which we did.
"We controlled the game in the first half of extra-time very, very well and then the sucker punch in the second half was a tough one to take. In fairness to the lads, I couldn’t speak highly enough of them."