Ajax had eliminated Real Madrid and Juventus in the past two rounds of the Champions League
Tottenham face a daunting task to keep their Champions League hopes alive after Ajax secured a crucial advantage in the semi-final first leg.
Donny van de Beek's 15th-minute goal, steered cleverly past Hugo Lloris from close range, put Erik ten Hag's exciting young side firmly in the driving seat going into the second leg in Amsterdam next Wednesday.
Spurs struggled to overcome the absence of forwards Harry Kane and Son Heung-min - injured and suspended respectively - and their job was made even harder by the loss of defender Jan Vertonghen after he suffered a facial injury in the first half.
Vertonghen's problem raised questions about player welfare after he was allowed to continue, albeit for only a few seconds, when he was clearly badly shaken up after an aerial collision involving team-mate Toby Alderweireld and Ajax goalkeeper Andre Onana. He eventually had to be supported by two members of the Spurs staff as he went off.
Tottenham tried to force the pace after the break with plenty of possession, but it was Ajax who came close to adding a second when David Neres struck the inside of the post with Lloris beaten.
Ajax held on to their lead in relative comfort and it will need a stirring Spurs comeback to prevent the Dutch side facing either Barcelona or Liverpool in the final on 1 June.
Spurs come up short
Tottenham were not lacking in effort on what many regarded as the biggest night in their history, a first Champions League semi-final staged in their magnificent new stadium.
It was quality and threat that was missing, with Spurs unable to compensate for the damaging suspension of Son and the injury to top goalscorer Kane.
The burden fell on to Christian Eriksen and Dele Alli, along with Lucas Moura, but they were simply unable to trouble Ajax on a night of pure frustration for manager Mauricio Pochettino, his players and the supporters who packed this arena and backed their team superbly.
Spurs also missed the midfield industry of the injured Harry Winks and were hit further by the loss of defender Vertonghen, who was surprisingly allowed to carry on briefly despite a heavy blow to the head and apparent questioning by referee Mateu Lahoz.
The Premier League side are still not out of this tie, and if their Champions League run to the last four has proved anything, it is that they must never be discounted.
However, they were second best and lacking in punch here. They will need to produce much better if their dream of advancing to the Champions League final in Madrid is to be realised.
Ajax show class and maturity
Ajax's advance to the Champions League semi-finals has made them the talk of European football after the manner in which they eliminated holders Real Madrid and Italian champions Juventus.
And it was easy to see what all the fuss is about as the visitors demonstrated maturity, composure and class in such a high-pressure environment to overcome Spurs.
Ajax took the game by the scruff of the neck early on, secured the goal their superiority deserved, then took the sting out of matters when required to close out the win.
Captain Matthijs de Ligt, just 19, showed leadership qualities beyond his years in defence, organising and ordering more experienced team-mates with expertise.
And in Barcelona-bound Frenkie de Jong, 21, and fellow midfielder Van de Beek, who is just a year older, this is an Ajax team with the class and youthful appearance that plays to this club's greatest traditions.
Ajax have almost come from nowhere after the group stages - but this is a team that looks like they have the quality and confidence to go all the way.
Man of the match - Frenkie de Jong (Ajax)Ajax midfielder Frenkie de Jong, who will join Barcelona this summer in a deal worth £65m, made 65 passes, with a pass accuracy of 86.2%, and also touched the ball 87 times - more than any other playerAjax score goal number 161 - the stats
English sides have lost just three of their past 30 home matches against Dutch opposition in European competition, with Spurs accounting for two of those defeats (also in March 2008 against PSV).Only one of the 17 previous teams to lose the first leg at home in a European Cup/Champions League semi-final has progressed into the final (Ajax in 1996).Ajax have scored in nine consecutive Champions League away games for the first time.Ajax have won their past four away games in the Champions League, having failed to win any of their previous 12.Tottenham had scored in their previous 20 Champions League games before Tuesday, with Ajax the first side to stop them scoring since Bayer Leverkusen in November 2016.Ajax have scored 161 goals this season, 63 more than Spurs (98).Ajax's Dusan Tadic has created 32 chances in the Champions League this season, the most by any player.The Dutch side's Nicolas Tagliafico has been shown twice as many yellow cards than any other player in the Champions League this season (six). Indeed, only Alessio Tacchinardi (nine, Juventus 2002-03) has been shown more yellows in a single campaign.'We are still alive' - what they said
Tottenham boss Mauricio Pochettino on BT Sport: "In the first half we did not start in a good way. Ajax showed more energy, it was difficult for us to play. It was our lack of energy.
"After we conceded the goal - 25 to 30 minutes in - we started to be in the game. Moussa Sissoko provided good energy.
"Second half we pushed them and tried to create chances. It was an even game in the second half.
"We are alive. It's only 1-0 down. We need to believe we can go there and win the game.
On playing with a five-man defence: "I can accept it was a mistake the shape we used - but there were not too many options. I am not happy - you cannot guess what happens if we play in a different way.
"It was the not the shape that conceded the goal. Our approach to the game was not good. I am the manager so I have responsibility."
On Vertonghen's head injury: "We will assess him in the next few days and we will see."
Champions League - your favourite football tournament?
Epic comebacks, record-breaking all-English classics, the world's biggest superstars... is the Champions League your favourite football tournament?
Do you prefer it to the World Cup, the Premier League with this season's incredible title race, La Liga or even the unpredictable EFL?
Tell us why. Get involved and contact us here.