Spurs were dead and buried at half-time in the second leg at the Johan Cryuff ArenA as they trailed their hosts 2-0 on the night and 3-0 on aggregate after goals from Matthijs De Ligt and Hakim Ziyech.
However, a miraculous comeback, spearheaded by Moura, was completed deep into added time when the Brazilian slotted home a loose ball to spark amazing scenes in Amsterdam.
It continues the remarkable progress for Spurs under boss Mauricio Pochettino, who has led the club further in Europe than any other.
Jurgen Klopp’s men may have thought their name was on the trophy after the manner of their comeback against Barcelona, but Spurs will have other ideas and it promises to be a brilliant spectacle in Madrid on June 1.
For Ajax, a brilliant run in this competition, where they beat Real Madrid and Juventus in previous rounds, ended in the most heartbreaking of ways and with their side set to be picked apart in the summer, they are unlikely to have a better chance of winning European football’s premier club competition than this.
“It’s still difficult to talk,” said Pochettino.
“Thank you football, thank you these guys, my players.
“This type of emotion without football I think is impossible to live.
“I am so grateful to be a coach and to be in football and to be living this type of moment.
“I think everyone deserves it in this club, with all the tough times we’ve had in the five years that we have been here.
“To have the chance to play a final is amazing. I want to remember my family, it is for them too.
“For the people who support us in that moment, it is amazing to reward them.
Pochettino also paid tribute to Lucas’ three-goal showing in Amsterdam.
“They are all heroes but he is a superhero,” he said.
“Unbelievable hat-trick. He deserves it, he is a great guy.”
Midfielder Christian Eriksen added: “I think it was a ridiculous game again.
“We were far down and we tried to fight back and in the end we were just lucky, lucky we scored.
“It’s a dream to reach the Champions League final. We wouldn’t have been able to look at ourselves in the mirror if we’d gone down 3-0 or 4-0.
“It was not tactical today, it was more of a fight, more heart.”
On hat-trick hero Lucas, Eriksen added: “I hope he gets a statue in England after this.”