The Dutch defender became the initial defender to score two goals in a Premier League match for Tottenham since Jan Vertonghen in spring 2013.
Key points
Micky Van de Ven nods into the net twice in first half
The home side's defender has goal disallowed after VAR review
Pape Matar Sarr scores final goal in 89th minute
This loss is the Merseyside club's first at Hill Dickinson Stadium
The Tottenham defender scored on two occasions as Spurs prolonged their winning streak in away games in the top division and delivered Everton their first defeat at Hill Dickinson Stadium.
Everton were undefeated in their five previous fixtures at their new ground at the dockside location, having departed Goodison Park behind after 133 years at the conclusion of last season.
But Spurs captain Van de Ven pounced on two occasions from corners in the opening 45 minutes to put their strong form at jeopardy, and they were unable to mount a comeback before Pape Matar Sarr - assisted by ex-Everton forward Richarlison - nodded in a third to put the game to bed.
Jake O'Brien thought he had equalized the tally a short while after Van de Ven's first goal, directing a bullet header past Guglielmo Vicario from an Everton corner.
Beto, in the meantime, missed a number of opportunities, while the Italian goalkeeper made a series of fine stops to ensure Tottenham went five matches on the road unbeaten in the Premier League.
But the VAR intervened, advising Craig Pawson to review the goal on the pitchside monitor and the official ruled that the winger and the attacker were in an illegal position and had impeded with the Tottenham goalkeeper.
This victory moves Thomas Frank's team up to third in the division, five points off north London rivals and leaders the Gunners.
Everton remain 14th and sit half a dozen points ahead of the relegation zone.
Following a uninspiring weekday performance in the European competition against Monaco, where they managed a mere two shots on target, the manager chose the French striker up front instead of former Toffees player the Brazilian.
The new arrival was unable to influence the game before being substituted for the substitute after 60 minutes on the pitch, but it turns out he wasn't needed in the final outcome.
Centre-back Van de Ven transformed into an attacking force to be feared.
Spurs' opening strike came from a cleverly executed corner routine, with Rodrigo Bentancur heading the ball back across the six-yard box for an free Van de Ven to score.
And the captain - filling in as captain in Cristian Romero's unavailability - added his second in added time as he rose above Jordan Pickford to nod in.
The Dutchman was just as impressive in defensive duties, partnering well with his defensive colleague as the pair handled superbly with the numerous deliveries sent their way by the opposition.
The club's new home had been a fortress, but it seems the novelty may have faded slightly and supporters headed to the exits after Sarr's third for Tottenham.
The break in Everton's winning streak at home won't be a massive worry for David Moyes, but their striker situation will be.
Beto and the other striker - the Toffees' two recognised strikers - had scored only one league goal combined before Sunday's match.
And they were unable to contribute to that poor tally on a wet and gloomy evening on in Liverpool.
Beto's form was summed up when he opted to overhead kick a golden opportunity from near the goal, despite having space and opportunity to reposition for a simpler attempt that would have challenged Vicario.
The substitute, as well, failed to make an impact after coming on for the starter in the 65th minute.
It wasn't for a lack of chance. Most of the home side's offensive moves came through the winger and the forward, who tirelessly delivered dangerous balls into the Spurs box.
The Toffees: Moyes' men head to the Stadium of Light in the top flight on Monday, 3 November at 8 PM.
Tottenham: Spurs travel to Newcastle's ground on late October for their fourth-round League Cup tie against Newcastle.
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