Ajax through Donny van de Beek scored the only goal of the game to give the Dutch side the advantage heading into the second leg of the semi-finals.
It was a fine performance from Ajax, whose young stars played some wonderful football at times and did a solid job defensively, especially in the second half.
Harry Kane (injured) and Son Heung-min (suspended) were both missing for Spurs and their absence was felt going forward.
Mauricio Pochettino’s side now have it all to do at the Johan Cruyff Arena as they chase their first ever Champions League final.
Just like they have all season, Ajax made a blistering start to the first half as they dominated Tottenham and created several chances.
And in the 15th minute, the Dutch side’s dominance paid dividends.
A lovely passing move saw Hakim Ziyech put Van de Beek through on goal with an inch-perfect through ball. Van de Beek had all the time in the world and made no mistake.
Nine minutes later the 22-year-old could have made it 2-0 but he shot straight at Hugo Lloris instead of squaring to a teammate.
As the game progressed Spurs slowly improved, with Fernando Llorente and Toby Alderweireld both meeting free-kicks from Kieran Tripper but heading off target.
One concern for Pochettino was the injury to Jan Vertonghen, who suffered a suspected broken nose after a collision with Alderweireld and was unable to continue.
Spurs came out much stronger in the second period and both sides had chances to score in a frantic opening five minutes.
Moussa Sissoko’s introduction in place of Vertonghen had a big impact, with the Frenchman’s pace and power helping to handle Ajax’s midfield.
But in the final third there just wasn’t enough from Tottenham. Lucas Moura had a quiet night, while Llorente and Dele Alli had opportunities to score but didn’t take them.
Spurs almost went 2-0 down in the 78th minute when David Neres’ shot looked to be heading for the bottom corner, but it hit the post.
One-nil was how it ended and Ajax’s players will be very confident of seeing out the tie at home next week.