Spurs came into the tie in good form in Europe on home soil with eight wins from the last 10, albeit only one win was at their new Tottenham Hotspur Stadium in the previous round against Manchester City.
But Ajax had already recorded impressive away leg wins this term, at both reigning champions Real Madrid and at Juventus in the quarter-finals. And it was easy to see why when they started brightly and took a deserved lead through Van de Beek inside the opening 15 minutes.
Spurs did enjoy the upper hand in spells either side of half-time, but struggled to really test Andre Onana in the Ajax goal, before the visitors stepped up a gear again.
It means the north Londoners have plenty of work to do in order to reach the final as Ajax take a slender lead and an away goal into next Wednesday’s second leg at the Johan Cruyff Arena in Amsterdam.
Tottenham boasted four changes from the side that lost 1-0 at home against West Ham on Saturday as Fernando Llorente came in for the suspended Son Heung-min, with Jan Vertonghen, Victor Wanyama and Kieran Trippier also handed starts.
Ajax boss Erik ten Hag made just one change from the side that beat Vitesse Arnhem last time out as David Neres replaced Kasper Dolberg in attack.
Spurs seemed happy to concede possession to Ajax in the early stages of the game and they were made to pay when the visitors took the lead after just 15 minutes.
Some excellent one-touch football ended with Hakim Ziyech threading the ball through to Van de Beek who coolly slotted his effort past Hugo Lloris as Spurs’ offside appeals were correctly rebuffed after the referee consulted with the Video Assistant Referee (VAR).
It should have been 2-0 on 24 minutes when, following another great move, Van de Beek saw his effort saved by Lloris while Dusan Tadic was waiting for a return pass which would have left him with a simple tap-in.
Spurs had their first effort two minutes later, but Llorente’s header from a Christian Eriksen free-kick dropped wide of the upright.
On 39 minutes, the hosts were then rocked by the loss of Vertonghen to a nasty facial injury following an aerial collision with team-mate Toby Alderweireld when looking to get on the end of an Eriksen set-piece.
Spurs did show some signs of life as the half came to a close with Alderweireld guiding a header just over the crossbar, before Vertonghen’s replacement Moussa Sissoko lashed a 30-yard strike wide.
Tottenham started the second half on the front foot but were almost caught out by a quick counter-attack with Nicolas Tagliafico firing a 25-yard effort inches wide of Lloris’ left-hand post.
Dele Alli had a shot comfortably saved by Onan, before the England international headed a Trippier cross over the top on 56 minutes.
Ajax appeared to weather the storm and started to impose themselves on the game again with Neres going so close to grabbing a second on 78 minutes when he collected a pass from Tadic on the edge of the area and hit a first-time strike across Lloris and off the far post.
Spurs did apply some late pressure in stoppage time with Juan Foyth’s cross into the area causing a moment of panic before Ajax could clear their lines, while Lucas Moura sliced an attempt wide with the goal in his sights.