The Dutch defender emerged as the initial backline player to net two goals in a Premier League game for Tottenham since Jan Vertonghen in spring 2013.
Match summary
The Spurs defender heads home twice in first half
Everton's Jake O'Brien has equalizer ruled after VAR review
Pape Matar Sarr nets third in 89th minute
The defeat is the Merseyside club's initial at their new ground
Micky van de Ven found the net on two occasions as Spurs extended their winning streak in away games in the top division and handed Everton their first defeat at their new home.
Everton were unbeaten in their last five matches at their new ground at Bramley-Moore Dock, having departed Goodison Park behind after 133 years at the end of the previous campaign.
But Spurs captain Van de Ven pounced twice from corners in the opening 45 minutes to put their strong form at risk, and they were failed to mount a comeback before Pape Matar Sarr - assisted by ex-Everton forward the Brazilian - nodded in a final goal to seal the victory.
Jake O'Brien believed he had equalized the tally a short while after Van de Ven's first goal, glancing a bullet header past the Spurs keeper from an Everton corner.
The Portuguese striker, meanwhile, failed to convert a number of chances, while the Italian goalkeeper made a succession of fine saves to guarantee Tottenham went five matches on the road unbeaten in the Premier League.
But the video assistant referee stepped in, instructing the match official to review the score on the pitchside monitor and the official ruled that Jack Grealish and Iliman Ndiaye were in an illegal position and had impeded with the Tottenham goalkeeper.
The win moves Thomas Frank's team into third place in the division, five points off local foes and leaders the Gunners.
Everton remain 14th and are six points ahead of the drop zone.
After a uninspiring weekday display in the European competition against the French side, where they managed a mere attempts on goal, the manager opted for Randal Kolo Muani in attack instead of ex-Everton forward Richarlison.
The summer signing was failed to make much of an impact before being replaced for the substitute after an hour on the field, but it emerged he proved unnecessary in the final outcome.
Centre-back Van de Ven converted into an attacking force to be feared.
Tottenham's first goal came from a well-worked corner routine, with Rodrigo Bentancur heading the ball toward the face of goal for an free the defender to score.
And the captain - filling in as skipper in Cristian Romero's absence - added his next goal in added time as he rose above Jordan Pickford to head home.
Van de Ven was just as impressive in defence, partnering well with Kevin Danso as the pair handled superbly with the 34 crosses thrown their way by the opposition.
The club's new home had been a happy hunting ground, but it appears the novelty may have faded slightly and fans headed to the exits after Sarr's final goal for Spurs.
The break in Everton's unbeaten home run won't be a major concern for David Moyes, but their striker situation will be.
The forward and Thierno Barry - the Everton's two established centre-forwards - had scored just one league goal combined before the weekend's outing.
And they were failed to contribute to that miserable tally on a damp and dreary evening on in Liverpool.
Beto's form was summed up when he chose to overhead kick a golden opportunity from close range, even with having room and opportunity to reposition for a more conventional shot that would have tested Vicario.
Barry, too, was unable to influence the game after replacing the starter in the second half.
It wasn't for a lack of opportunity. Most of the home side's attacks came through Grealish and the forward, who relentlessly whipped dangerous balls into the Tottenham penalty area.
Everton: Moyes' men travel to Sunderland in the Premier League on Monday, 3 November at 8 PM.
Spurs: Spurs go to St James' Park on late October for their next round League Cup tie against Newcastle.
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