More than three decades on and they still talk about the time when Johan Cruyff came to White Hart Lane and was outclassed by Glenn Hoddle.
Cruyff was in the twilight of his career and playing for Feyenoord but the occasion left an impression.
This one did, too, as Ajax continued to blossom, a nascent team which will never be given the chance to mature, with youngsters tipped for great things at wealthier clubs.
Donny van de Beek deservedly gave Ajax the lead in the first half on Tuesday evening
Fearless and high on the confidence of beating Real Madrid and Juventus, they were too good for a Tottenham side feeling the strain and depleted by injuries.
Whether that weekend of rest made much difference to the energy tanks is arguable but one team looked much fresher and sharper when the seal was broken on this semi-final.
Reach for the moon said Mauricio Pochettino but his trio of former Ajax centre-halves were soon were gasping for air.
Davinson Sanchez seemed to have his head in a spin, his game littered with errors, bewildered by the breath-taking pace and mobility before him.
Jan Vertonghen had to go off after a nasty collision with his team-mate Toby Alderweireld
Toby Alderweireld’s customary cool was lost and Jan Vertonghen was seeing stars when he collided with goalkeeper Andre Onana in the first half.
For Spurs, this European campaign has been a protracted test of character from the first fixture when they turned victory into defeat in the final few minutes at Inter Milan.
They were five minutes from an exit in Barcelona and nerves were shred at Manchester City.
Last night, they were challenged to find extra depths of resolve. This was about defensive focus while under intense pressure and made more difficult by the fact there was no outlet.
Without Heung-min Son to keep the ball and give them a breather or Harry Kane to worry the Ajax defenders.
Frenkie de Jong has a real understanding of the game and controlled the midfield for Ajax
The Dutchman celebrates with Dusan Tadic following their opening goal against Tottenham
Tottenham have conceded a precious away goal and will face an uphill struggle in the flatlands of Holland but their major triumph was to hang on and remain in the tie at all.
It could have been all over.
For half an hour it appeared destined to slide out of reach as Frenkie de Jong and Donny dan ve Beek seized control in midfield.
De Jong has already inspired claims he has the talent to be as influential as Cruyff as he prepares to follow the same path from Amsterdam to Barcelona.
Spurs tried to sign him last year, searching for a successor to Mousa Dembele but could not compete when he agreed a £75m move to the Nou Camp at the end of this season.
At 21, his composure and understanding is striking; his awareness and appreciation of the blur of movement ahead of him in this team.
De Jong was given too much time on the ball with Dele Alli having a poor opening 30 minutes
De Jong has inspired claims he has the talent to be as influential as Dutch legend Johan Cruyff
One moment in the opening minutes caught the eye when he nonchalantly eased the ball over his own shoulder on the volley to the feet of centre-half Matthijs de Ligt.
Pochettino may regret his decision to start with a back-three but at the time it was understandable, based on the absence of midfielders and strikers.
But his team were overrun in midfield and forced deep, where they proved vulnerable to the high-pressing intensity of the visitors and the speed of their front men.
Spurs were messy but Ajax deserved their lead and probably deserved more.
Pochettino at least spotting the problem and stepped forward to help, changing the shape after 30 minutes, reverting to a back four and the long interruption to treat Vertonghen’s head injury knocked the Dutch from their silky rhythm.
Alli has had a difficult season and rarely threatened Ajax’s defence during this first leg clash
The Spurs boss took the chance to send on Moussa Sissoko, who was not deemed fit enough to start after injury, rather than Ben Davies when he lost Vertonghen.
Sissoko supplied presence and, with it, more resistance in midfield and Dele Alli was unleashed, immediately more influential in a more advanced role, trying to play off the knock downs from Fernando Llorente and link up with Lucas Moura.
Alli, only a year older than De Jong, is approaching the end of his fourth season as a Spurs player and it has been a difficult one, after a successful World Cup with England and the disruption of injuries.
He has been playing in a lightweight cast to protect two broken bones in his left hand and has scored only once since Christmas.
Alli often rises to the big games but he was lost starting in a deeper role.
Tottenham fared much better in the second half as they went direct to Fernando Llorente
By the time he was released to play further forward, Ajax had adopted a more conservative approach and were able to smother him around the edges of the penalty area.
Tottenham improved after the interval but their greatest threat came from set-pieces and aerial attacks with an element of old-fashioned England against the Dutch total football.
Pochettino’s team fought back and can claim but this was not destined to go down as the night when De Jong was eclipsed by Sissoko.
This was a night to admire the Ajax and their fabulous young team and to offer some credit to Spurs for fighting to survive, even when they were outclassed.
Mauricio Pochettino’s men were outclassed by Ajax’s youthful side but clung on to retain hope