The Dutch defender became the first backline player to score two goals in a English top-flight game for Tottenham since Jan Vertonghen in spring 2013.
Key points
Micky Van de Ven nods into the net twice in first half
Everton's defender has equalizer ruled after VAR review
Senegalese midfielder scores third in dying moments
The defeat is the Merseyside club's first at Hill Dickinson Stadium
The Tottenham defender scored on two occasions as Tottenham prolonged their winning streak on the road in the top division and handed the Toffees their initial loss at their new home.
Everton were undefeated in their last five matches at their new ground at the dockside location, having departed Goodison Park behind after more than a century at the conclusion of the previous campaign.
But Tottenham's leader Van de Ven struck twice from set-pieces in the first half to place their impressive record at risk, and they were unable to turn it around before the midfielder - set up by former Toffees attacker the Brazilian - headed home a final goal to seal the victory.
Jake O'Brien thought he had levelled the tally a short while after Van de Ven's opener, glancing a bullet header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, in the meantime, missed a number of opportunities, while Vicario made a series of excellent saves to guarantee the London club went five away games unbeaten in the Premier League.
But the VAR intervened, advising the match official to check the score on the pitchside monitor and the referee ruled that the winger and the attacker were in offside positions and had interfered with the Spurs keeper.
This victory moves Thomas Frank's team up to third in the division, a handful of points off north London rivals and table-toppers the Gunners.
Everton stay in 14th position and are half a dozen points ahead of the relegation zone.
After a drab weekday performance in the Champions League against the French side, where they mustered a only attempts on target, the manager chose the French striker up front instead of former Toffees player the Brazilian.
The new arrival was failed to make much of an impact before being replaced for Richarlison after an hour on the field, but it turns out he wasn't needed in the end.
Defender Van de Ven converted into an offensive threat to be reckoned with.
Spurs' first goal came from a cleverly executed set-piece play, with Rodrigo Bentancur heading the ball toward the six-yard box for an free Van de Ven to score.
And the captain - filling in as skipper in the Argentine's absence - notched his next goal in added time as he outjumped Jordan Pickford to nod in.
Van de Ven was just as impressive in defence, partnering well with his defensive colleague as the pair dealt superbly with the 34 crosses thrown their way by Everton.
The club's new home had been a fortress, but it seems the freshness may have worn off slightly and supporters headed to the gates after Sarr's final goal for Spurs.
The end in the team's unbeaten home run won't be a major worry for David Moyes, but their striker situation will be.
The forward and Thierno Barry - the Toffees' two established 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 Merseyside.
Beto's form was epitomized when he chose to bicycle-kick a golden opportunity from near the goal, even with having room and time to reposition for a simpler attempt that would have tested the keeper.
The substitute, too, failed to make an impact after coming on for the starter in the 65th minute.
It was not for a lack of chance. The majority of the home side's attacks came through Grealish and Ndiaye, who tirelessly whipped threatening balls into the Spurs penalty area.
The Toffees: The team travel to the Stadium of Light in the Premier League on early November at 8 PM.
Spurs: The London club go to Newcastle's ground on late October for their fourth-round Carabao Cup tie against the Magpies.
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Cynthia Jones
Cynthia Jones
Cynthia Jones
Cynthia Jones
Cynthia Jones