Spurs, at this stage of the competition for the first time in over half a century, were overwhelmed in the opening stages and fortunate that Ajax's intricate passing and movement only resulted in the one goal.
Van de Beek scored that, having gathered Hakim Ziyech's precise pass before sitting down Hugo Lloris with a couple of feints prior to his finish.
The Eredivisie leaders almost scored a second on Tuesday only for David Neres' late effort to come back off a post, but they still took charge of the tie ahead of the return leg in Amsterdam next week.
Ajax wasted no time at all in stamping their authority on the contest and it was no surprise to see them take the lead in the 15th minute.
Van de Beek, involved earlier in the move when he brilliantly flicked the ball away from Dele Alli, drifted between Jan Vertonghen and Danny Rose, collected Ziyech's pass and calmly placed his finish beyond Lloris.
There was no need for a VAR check as replays showed the midfielder was marginally onside and Ajax kept their foot on the accelerator, with Rose almost slicing into his own net and Van de Beek being denied by Lloris at his near post following a fine dummy.
Spurs eventually responded and looked most threatening from free-kicks, Fernando Llorente and then Toby Alderweireld both directing Kieran Trippier set-pieces off target.
Yet, already shorn of the injured Harry Kane and suspended Son Heung-min, they were forced to reorganise again when a battered and bloodied Vertonghen had to come off having collided with Alderweireld's head.
That enforced introduction of Moussa Sissoko gave Spurs more midfield control and Alli twice came close before the hour, firing a volley straight at Andre Onana and then heading over.
Yet opportunities such as those who were too infrequent from the hosts' perspective as their defensive work in chasing Ajax early on appeared to take its toll.
And they were fortunate the Dutch club did not leave London with a greater advantage as Neres' placed finish from a counter-attack with 12 minutes to go came back off a post with Lloris motionless.
What does it mean? Giant-killers Ajax on top
Ajax have already knocked out holders Real Madrid and Juventus in the knockout stages of this competition, and they were not in front after either of the first legs of those ties. Yet Spurs will take some confidence from the way they responded to Ajax's strong start. Plus, they get Son back for the game in Amsterdam next Wednesday, when they will need to score at least one.
Donny's day in north London
Frenkie de Jong and Matthijs de Ligt, who have rightly garnered so much praise during Ajax's run, again impressed but attacking midfielder Van de Beek further enhanced his reputation with another terrific display. As well as his goal, he made two key passes, had more shots than anyone in his team and his movement and sharp touches meant Spurs' midfielders appeared to be forever chasing his shadow.
22y 12d - Donny van de Beek (22y 12d) is the third youngest Ajax goalscorer in a Champions League semi-final after Nordin Wooter (19y 237d) and Mario Melchiot (20y 170d). Stunned. #TOTAJA pic.twitter.com/RFB6pryTjU— OptaJoe (@OptaJoe) April 30, 2019
Torrid night for Trippier
As expected, Ajax exposed Tottenham down the flanks and Spurs' overrun right wing-back Trippier, in particular, struggled to handle Neres and Nicolas Tagliafico, albeit with little assistance. Crucially, it was Trippier who played Van de Beek onside for his 15th-minute goal.
Key Opta Facts:
- Only one of the 17 previous teams to lose the first leg at home in a European Cup/Champions League semi-final tie has progressed into the final (Ajax in 1995-96).
- Ajax have scored in nine consecutive Champions League away games for the first time in their history.
- After failing to win any of their previous 12 Champions League away games (D6 L6), Ajax have won their last four in a row; their longest winning run on the road in the competition since March 1997 (7).
- Tottenham had scored in each of their previous 20 Champions League games prior to this game, with Ajax the first side to stop them scoring since Bayer Leverkusen in November 2016 (0-1).
- Ajax's Dusan Tadic has created 32 chances in the Champions League this season, the most of any player.
Prior to the return leg, Tottenham can secure a top-four berth in the Premier League – and qualification for next year's Champions League – with victory at Bournemouth on Saturday. Treble-seeking Ajax, top of the Eredivisie but level on points with PSV, are away to Willem II in the domestic cup final on Sunday.