Heading into the game 1-0 up on aggregate, the home team appeared in cruise control at Johan Cruyff Arena after taking a 2-0 lead on the night through an early headed goal from teenage skipper Matthijs de Ligt and a smart strike from Hakim Ziyech.
But the Dutch side were forced into a nerve-jangling finale after Moura scored twice in the space of five second-half minutes, with Spurs somehow clawing themselves back into the tie with half an hour to play.
The Premier League club pressed relentlessly in the closing stages while surviving scares at the other end, and pulled off a footballing miracle when Moura completed his hat-trick deep into injury time to send them into the final against Liverpool.
AFTER ANFIELD, ANOTHER CLASSIC
After barely-believable drama at Anfield on Tuesday night, Spurs and Ajax followed suit by serving up another Champions League classic.
The home team opened in typically nerveless fashion and found themselves 1-0 up after just five minutes when 19-year-old skipper de Ligt headed home from a corner.
They doubled their lead half an hour later when Ziyech finished a smart move, whipping the ball left-footed across Hugo Lloris and into the corner of the net.
They went into the break 2-0 up and 3-0 to the good overall, with one foot seemingly in the final.
The strains of Bob Marley’s ‘Don’t Worry ‘bout a Thing’ played out around Johan Cruyff Arena before the start of the second half, and it had certainly been a carefree first-half showing from the hosts.
But Mauricio Pochettino’s Spurs team showed their guts against Manchester City in the last round, and set about reversing the odds again in the Dutch capital.
They first pulled one back on 55 minutes, when a lightning-quick break saw Dele Alli race clear and weave his way through before Moura took over, riding a challenge before slotting calmly past Andre Onana.
Just four minutes later he had a second, making the most of a mix-up after Onana saved a shot from substitute Fernando Llorente and then turning and shooting home in a crowded box.
The match swung back and forth and both teams had chances, but it was left to Moura to settle it deep into injury time when he fired home from the edge of the box to put Spurs 3-2 up on the night and into the final on away goals.
Thoughts will be spared for this young Ajax team, many of whom lay distraught on the turf at the final whistle. They have provided so many memorable moments in this year’s competition, only to fall agonizingly short at the penultimate hurdle.
For Spurs, the formidable force of Liverpool now await in the final in Madrid on June 1, but for now the London club will care little – and fear no one – after what was yet another night of unbelievable Champions League drama.