Trailing 2-0 at the interval and 3-0 overall, Moura scored three times in the second half, including a last-gasp winner, to set up an all-English final against Liverpool in Madrid next month.
“It’s impossible to explain what I’m feeling,” Brazilian Moura told BT Sport after the game on Wednesday.
“We gave everything on the pitch and deserved this moment — we are family.
“Football is amazing, its gives us moments like this. We cannot imagine. It’s the best moment in my life, and in my career.”
Such a scoreline seemed unfathomable when Ajax moved two goals ahead on the night inside the opening 35 minutes courtesy of Matthijs de Ligt’s header and Hakim Ziyech’s fine strike.
But Tottenham roared back after the interval with Moura scoring twice in four minutes to drag his side level on the night as Ajax began to wilt under constant waves of pressure.
And as the game moved into the final minute of stoppage time, Moura produced another moment of magic to send Tottenham through and leave this young Ajax side stunned.
But it was not just Dutch faces with tears streaming down their faces. Mauricio Pochettino, the Tottenham coach, cried with the sheer emotion of the achievement clearly too much for him to handle.
Wiping away the tears, Pochettino paid tribute to his players after their remarkable second-half showing.
“Thank you football,” he told BT Sport. “My players are heroes. I’m so emotional now. It’s an amazing moment, it’s difficult to describe in words.
“When you work, when you feel the love, it’s not a stress. It’s a passion and we showed that passion.”
Lightning strikes twice
For the second night in succession, football’s ability to constantly shock and surprise came to the fore.
Even after the events at Anfield 24 hours earlier, where Liverpool had fought back from a three-goal first leg deficit to overcome Barcelona by winning 4-0 on the night, 4-3 on aggregate, few believed Tottenham could achieve similar feats especially after a nightmare opening period.
For Ajax, this will be a night that will live long in the memory, the night it somehow contrived to throw away the opportunity of a first Champions League final since 1996.
Quite how it managed to fritter away a two-goal lead on the night and a three-goal advantage overall will no doubt be discussed until the early morning across the bars of Amsterdam.
For 45 minutes at least, this was Ajax’s opportunity. This team of young players had already surpassed all expectations in defeating Real Madrid and Juventus on its way to the last four of the competition.
Few other teams have entertained like Ajax this season, its group of young players seemingly unperturbed by the pressure, playing a brand of football that excites and thrills at every opportunity. And for the first half in Amsterdam, that’s what it did.
In fact, it took just five minutes for the precociously talented De Ligt to give Ajax the lead, heading home unopposed before running off to celebrate. At just 19 he is frightening prospect, a player who surely will have the opportunity to win the Champions League later in his career.
But few would have begrudged him the chance to dream about lifting the trophy when Ziyech added a second after 35 minutes, firing an exquisite effort beyond the despairing dive of Hugo Lloris to make it 2-0 on the night and 3-0 on aggregate. Tottenham looked finished.
At the start of the second half, Ajax fans joyously sang the Bob Marley’s “Everything’s Gonna Be Alright.”
Ajax, for so much of the season the underdog, the team that had consistently defied the odds against the so-called bigger sides, began to sense glory.
For the first time in this year’s competition, the pressure was on Ajax. It had become the bigger team. The expectation had ballooned. This was the moment.
While supporters in the stands may have afforded themselves a quick glance at flight prices from Amsterdam to Madrid, or a hotel room in the Spanish capital, Tottenham had other ideas.
Fernando Llorente had come on at the start of the second half and the Spurs striker’s physical presence and ability to win aerial duels began to unsettle Ajax.
Tottenham signalled its intention that they weren’t done as Dele Alli produced a fine through ball for Moura to run onto a steer his effort past the onrushing Andre Onana in the Ajax goal.
Four minutes later, Tottenham drew level on the night as Moura displayed fabulous skill to control the ball inside the penalty area before rifling the ball past Onana once again.
Shell-shocked, Ajax tried to respond.
Both teams, by now clearly exhausted and drunk on emotion, poured forward in a frantic end to the contest.
Ziyech, who was hugely impressive throughout, went close for the home side hitting the post with a shot as Tottenham left space in behind in an attempt to find a winner.
But that winner appeared to have escaped from its clutches when Jan Vertonghen could only send his header against the crossbar before having his subsequent effort blocked on the line.
When the fourth official signaled a minimum of five minutes of stoppage time to be play, Ajax’s players appeared to collectively shrink by an inch.
Tottenham sensed its moment and once again it was Moura with the final meaningful kick of the contest, driving a stake through Ajax hearts by firing home from 16-yards.
Cue silence but for a few thousand souls from north London, drunk on delirium and no doubt a beer or two who must have had to pinch themselves to make sure it was real.
Tottenham, for so long derided as a club who fail at the final hurdle, for whom the definition of ‘Spursy’ was invented, had cast aside all doubters and triumphed when it had no right to do so.
After June 1, those doubters may be silenced for good.