Here, AFP Sport looks at three things we learned from the Johan Cruyff Arena clash:
When Lucas Moura played kick-about with his one-year-old son on the pitch at the Tottenham Hotspur Stadium after his hat-trick against Huddersfield in April, it seemed the Brazilian forward's season had reached its high point.
But the 26-year-old's treble in that low-key 4-0 win was just the start of a remarkable end to the season for the unsung hero whose incredible hat-trick broke Ajax hearts.
Unwanted by Paris Saint Germain, who sold him to Tottenham in January 2018, Lucas was a bit-part player for much of his first season in north London.
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In a testimony to his strength of character, he refused to be marginalised again this term and quickly proved his worth with a brace in Tottenham's win at Manchester United in August.
By the time injury sidelined Harry Kane in the Champions League quarter-finals, Lucas was primed and ready to seize his chance.
However, even Lucas would have been forgiven more pinching himself if he had learned how his trip to Amsterdam would turn out.
With Tottenham two down on the night and three goals behind on aggregate, all looked lost.
But Dele Alli's clever turn and pass into the area sent Lucas sprinting through for a cool finish past Andre Onana to give Tottenham an unexpected lifeline in the 55th minute.
Four minutes later they punished more nervous defending from Ajax to strike again as Lucas spun around to drive into the corner after Fernando Llorente's close-range effort was pushed out by Onana.
It was Lucas's fourth goal in the competition this season, his latest priceless contribution coming after he also scored the late equaliser in Barcelona that ensured their progress from the group stage.
And with just seconds left in Tottenham's semi-final escape bid, he pounced on Alli's pass to drill a fierce winner into the far corner.
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Alongside Danny Blanchflower, Glenn Hoddle, Paul Gascoigne and Ricky Villa, Lucas will now forever be enshrined as a Tottenham legend.
With just 45 minutes standing between Ajax and their first Champions League final since 1996, the Dutch club were engulfed by a fatal wave of arrogance.
As the half-time whistle blew, Ajax players, including Hakim Ziyech, could be seen grinning from ear to ear as they contemplated their surely inevitable progress to the Madrid showpiece.
They were leading by three goals on aggregate after scoring twice in the first half to leave Tottenham on the brink.
Such was the confidence pumping through the raucous arena that before the second half began, the entire crowd, including Ajax great Patrick Kluivert, engaged in a mass singalong to Bob Marley's 'Don't Worry About a Thing'.
The chant continued into the opening seconds of the half, but that rock-solid belief was quickly shattered as Lucas struck twice in a matter of minutes to send shock-waves through the Ajax team and their now less boisterous supporters.
The panic was palpable and Ajax couldn't recover as waves of Tottenham attacks culminated in Lucas's dramatic winner.
It was a bitter end to a breakthrough campaign for Ajax's young guns, who had beaten Real Madrid and Juventus en route to the last four.
Speaking on the eve of the second leg, Mauricio Pochettino uttered a prediction that will rank among the most prescient in Tottenham's history.
Asked if his side would go for broke right from the start as they tried to overturn that one-goal deficit, the Tottenham manager replied: "We could win it in the first minute or the last minute."
Pochettino's gambit was spot on as Lucas's stoppage-time strike fired Tottenham through to an all-Premier League final against Liverpool in Madrid on June 1.
It was a tour de force for the emotional Pochettino, who turned the game in Tottenham's favour by sending on Spanish striker Fernando Llorente at half-time.
The Argentine wept uncontrollably at the final whistle as Tottenham celebrated becoming only the second team to reach the final after losing the first leg at home.
Tottenham's first European final since they won the 1984 UEFA Cup also offers Pochettino a chance to win his first trophy as a manager.
Pochettino made the staggering admission this week that he would consider quitting if Tottenham were to lift the Champions League.
Surely Tottenham chairman Daniel Levy wouldn't let him get anywhere near the exit door after this miraculous triumph.
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