The Dutch defender emerged as the first backline player to score two goals in a Premier League match for Spurs since the Belgian defender in spring 2013.
Match summary
Micky Van de Ven heads into the net two times in opening period
Everton's Jake O'Brien has goal ruled after VAR review
Pape Matar Sarr scores final goal in 89th minute
This loss is Everton's initial at their new ground
The Tottenham defender scored on two occasions as Spurs extended their winning streak in away games in the top division and handed Everton their initial loss at their new home.
The Toffees were undefeated in their last five matches at their new ground at Bramley-Moore Dock, having left Goodison Park behind after 133 years at the conclusion of the previous campaign.
But Spurs captain Van de Ven struck on two occasions from set-pieces in the opening 45 minutes to place their impressive record at risk, and they were unable to mount a comeback before Pape Matar Sarr - assisted by former Toffees attacker the Brazilian - headed home a final goal to seal the victory.
Jake O'Brien believed he had equalized the scores a short while after Van de Ven's opener, glancing a bullet header past Guglielmo Vicario from an set-piece.
Beto, in the meantime, missed a number of opportunities, while the Italian goalkeeper made a succession of fine stops to guarantee Tottenham went five matches on the road without defeat in the Premier League.
But the VAR intervened, advising the match official to check the goal on the pitchside monitor and the referee ruled that Jack Grealish and the attacker were in an illegal position and had impeded with the Tottenham goalkeeper.
The win elevates the manager's team into third place in the division, a handful of points off north London rivals and leaders Arsenal.
The Merseyside club stay 14th and sit six points clear of the drop zone.
After a drab midweek performance in the European competition against Monaco, where they managed a only attempts on goal, the manager chose the French striker up front instead of former Toffees player the Brazilian.
The summer signing was failed to influence the game before being replaced for the substitute after an hour on the field, but it emerged he proved unnecessary in the end.
Defender the Dutchman transformed into an attacking force to be reckoned with.
Tottenham's opening strike came from a cleverly executed corner routine, with the midfielder directing the ball toward the six-yard box for an unmarked Van de Ven to head home.
And Ven de Ven - stepping up as captain in Cristian Romero's absence - notched his second in first-half stoppage time as he outjumped the England keeper to nod in.
The Dutchman was equally impressive in defence, combining effectively with Kevin Danso as the duo handled excellently with the numerous deliveries thrown their way by Everton.
The club's new home had been a happy hunting ground, but it appears the novelty may have faded somewhat and supporters headed to the gates after the midfielder's third for Tottenham.
The break in the team's winning streak at home won't be a major concern for David Moyes, but their attacking woes will be.
The forward and the other striker - the Everton's two recognised strikers - had netted only a single goal combined before the weekend's match.
And they were unable to contribute to that poor tally on a damp and dreary evening on Merseyside.
Beto's performance was summed up when he opted to bicycle-kick a clear chance from near the goal, even with having space and time to reposition for a more conventional shot that would have challenged the keeper.
Barry, too, was unable to influence the game after replacing the starter in the second half.
It was not for a lack of opportunity. Most of Everton's offensive moves came through the winger and Ndiaye, who relentlessly whipped threatening crosses into the Spurs box.
Everton: The team travel to Sunderland in the Premier League on early November at 20:00 GMT.
Spurs: Spurs go to St James' Park on late October for their fourth-round League Cup match against Newcastle.
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