The Dutch defender emerged as the first backline player to net two goals in a Premier League game for Spurs since Jan Vertonghen in spring 2013.
Key points
The Spurs defender nods into the net two times in first half
The home side's Jake O'Brien has equalizer ruled after VAR review
Senegalese midfielder nets final goal in 89th minute
This loss is Everton's first at their new ground
The Tottenham defender found the net on two occasions as Spurs extended their winning streak on the road in the Premier League and handed the Toffees their initial loss at their new home.
The Toffees were undefeated in their five previous fixtures at their new ground at Bramley-Moore Dock, having left their historic home behind after 133 years at the conclusion of last season.
But Tottenham's leader Van de Ven pounced twice from corners in the opening 45 minutes to place their impressive record at risk, and they were unable to turn it around before Pape Matar Sarr - set up by former Toffees attacker Richarlison - nodded in a final goal to seal the victory.
Jake O'Brien thought he had levelled the scores a short while after the defender's first goal, directing a powerful header past the Spurs keeper from an set-piece.
The Portuguese striker, meanwhile, failed to convert a handful of opportunities, while the Italian goalkeeper made a succession of excellent stops to ensure the London club went five away games unbeaten in the English top flight.
But the VAR stepped in, advising the match official to check the goal on the pitchside monitor and the official decided that Jack Grealish and Iliman Ndiaye were in offside positions and had impeded with the Spurs keeper.
The win elevates Thomas Frank's side into third place in the division, a handful of points off north London rivals and leaders Arsenal.
Everton remain 14th and are half a dozen points ahead of the drop zone.
After a drab weekday display in the European competition against the French side, where they mustered a mere two shots on goal, Frank chose the French striker up front instead of ex-Everton forward Richarlison.
The summer signing was failed to make much of an impact before being substituted for Richarlison after an hour on the field, but it emerged he wasn't needed in the end.
Centre-back Van de Ven converted into an attacking force to be feared.
Tottenham's opening strike came from a well-worked set-piece play, with Rodrigo Bentancur directing the ball toward the face of goal for an unmarked Van de Ven to score.
And the captain - stepping up as skipper in the Argentine's absence - added his second in first-half stoppage time as he rose above Jordan Pickford to head home.
The Dutchman was equally impressive in defensive duties, partnering effectively with his defensive colleague as the pair dealt excellently with the 34 crosses sent their way by Everton.
The club's new home had been a fortress, but it appears the freshness may have worn off somewhat and supporters flocked to the gates after Sarr's third for Tottenham.
The break in Everton's winning streak at home will not be a major concern for David Moyes, but their attacking woes are.
The forward and Thierno Barry - the Everton's two recognised centre-forwards - had scored only one league goal combined before the weekend's outing.
And they were unable to add to that poor tally on a wet and gloomy night on Merseyside.
The striker's performance was summed up when he chose to overhead kick a clear chance from near the goal, even with having room and opportunity to readjust for a simpler attempt that would have tested Vicario.
Barry, as well, failed to make an impact after replacing the starter in the second half.
It was not for a lack of opportunity. Most of the home side's offensive moves came through Grealish and the forward, who relentlessly delivered threatening balls into the Tottenham penalty area.
Everton: The team head to the Stadium of Light in the top flight on Monday, 3 November at 20:00 GMT.
Spurs: Spurs go to St James' Park on late October for their fourth-round Carabao Cup tie against the Magpies.
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