The Dutch defender became the first defender to net two goals in a English top-flight match for Tottenham since the Belgian defender in March 2013.
At a glance
Micky Van de Ven nods home two times in opening period
The home side's defender has equalizer disallowed after VAR review
Senegalese midfielder nets third in dying moments
The defeat is the Merseyside club's initial at their new ground
The Tottenham defender scored twice as Tottenham extended their unbeaten run in away games in the Premier League and delivered Everton their first defeat at Hill Dickinson Stadium.
Everton were unbeaten in their five previous fixtures at their new ground at the dockside location, having departed their historic home behind after 133 years at the conclusion of last season.
But Tottenham's leader the Dutchman struck twice from corners in the first half to place their strong form at jeopardy, and they were unable to mount a comeback before Pape Matar Sarr - set up by ex-Everton forward the Brazilian - nodded in a final goal to put the game to bed.
The Everton defender thought he had equalized the scores a short while after the defender's opener, directing a powerful header past the Spurs keeper from an set-piece.
The Portuguese striker, in the meantime, missed a handful of chances, while the Italian goalkeeper made a succession of fine stops to ensure the London club went five matches on the road unbeaten in the Premier League.
But the VAR stepped in, instructing the match official to review the goal on the pitchside monitor and the referee ruled that the winger and Iliman Ndiaye were in an illegal position and had impeded with the Spurs keeper.
The win moves the manager's side up to third in the Premier League, a handful of points off local foes and leaders Arsenal.
The Merseyside club remain 14th and are six points clear of the drop zone.
Following a uninspiring weekday performance in the European competition against the French side, where they mustered a mere attempts on target, the manager chose the French striker in attack instead of former Toffees player the Brazilian.
The new arrival was unable to influence the game before being replaced for Richarlison after 60 minutes on the field, but it emerged he proved unnecessary in the final outcome.
Centre-back the Dutchman converted into an attacking force to be reckoned with.
Tottenham's first goal came from a well-worked set-piece play, with the midfielder directing the ball back across the six-yard box for an unmarked Van de Ven to score.
And Ven de Ven - filling in as captain in Cristian Romero's absence - added his second in first-half stoppage time as he rose above Jordan Pickford to nod in.
The Dutchman was equally outstanding in defence, combining well with Kevin Danso as the pair handled excellently with the 34 crosses thrown their way by Everton.
The club's recent stadium had been a fortress, but it appears the novelty may have faded somewhat and supporters headed to the exits after the midfielder's third for Spurs.
The end in the team's unbeaten home run won't be a massive concern for David Moyes, but their attacking woes are.
Beto and Thierno Barry - the Toffees' pair of recognised centre-forwards - had netted just one league goal combined before Sunday's outing.
And they were failed to contribute to that poor record on a wet and gloomy evening on in Liverpool.
Beto's form was summed up when he chose to bicycle-kick a golden opportunity from close range, even with having space and opportunity to reposition for a simpler attempt that would have tested Vicario.
Barry, as well, failed to influence the game after coming on for the starter in the second half.
It was not for a lack of opportunity. Most of Everton's attacks came through Grealish and the forward, who tirelessly delivered dangerous crosses into the Tottenham box.
Everton: Moyes' men head to the Stadium of Light in the Premier League on Monday, 3 November at 8 PM.
Tottenham: Spurs travel to Newcastle's ground on Wednesday, 29 October for their fourth-round League Cup match against Newcastle.
Elena Vance is a tech strategist with over a decade of experience in digital transformation and business analytics.