The Dutch defender became the first defender to net two goals in a English top-flight match for Tottenham since Jan Vertonghen in spring 2013.
At a glance
Micky Van de Ven heads home twice in opening period
The home side's defender has goal disallowed after video check
Senegalese midfielder nets third in dying moments
The defeat is Everton's initial at Hill Dickinson Stadium
Micky van de Ven found the net on two occasions as Tottenham prolonged their winning streak on the road in the top division and delivered the Toffees their initial loss at Hill Dickinson Stadium.
Everton were undefeated in their five previous fixtures at their new ground at Bramley-Moore Dock, having left their historic home behind after more than a century at the end of last season.
But Spurs captain Van de Ven pounced twice from corners in the opening 45 minutes to place their strong form at risk, and they were unable to mount a comeback before the midfielder - set up by former Toffees attacker Richarlison - nodded in a final goal to put the game to bed.
The Everton defender thought he had levelled 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, missed a handful of chances, while the Italian goalkeeper made a series of fine saves to ensure Tottenham went five away games unbeaten in the English top flight.
But the video assistant referee intervened, instructing the match official to review the score on the pitchside monitor and the official decided that the winger and the attacker were in offside positions and had interfered with the Spurs keeper.
The win moves Thomas Frank's side up to third in the Premier League, five points off local foes and leaders the Gunners.
The Merseyside club remain in 14th position and are six points clear of the drop zone.
Following a uninspiring weekday performance in the Champions League against the French side, where they mustered a only attempts on goal, the manager opted for Randal Kolo Muani up front instead of former Toffees player the Brazilian.
The new arrival was failed to make much of an impact before being replaced for the substitute after an hour on the pitch, but it emerged he proved unnecessary in the end.
Centre-back the Dutchman transformed into an attacking force to be reckoned with.
Spurs' first goal came from a well-worked corner routine, with Rodrigo Bentancur heading the ball toward the face of goal for an free Van de Ven to score.
And the captain - stepping up as captain in the Argentine's absence - notched his second in added time as he outjumped Jordan Pickford to head home.
Van de Ven was just as outstanding in defensive duties, partnering well with his defensive colleague as the duo dealt excellently with the numerous deliveries thrown their way by Everton.
Everton's new home had been a fortress, but it appears the novelty may have worn off somewhat and fans headed to the exits after Sarr's final goal for Tottenham.
The break in Everton's unbeaten home run won't be a massive concern for the manager, but their striker situation are.
The forward and Thierno Barry - the Everton's pair of established strikers - had netted only one league goal between them before the weekend's match.
And they were failed to contribute to that poor tally on a damp and dreary evening on Merseyside.
Beto's performance was epitomized when he opted to overhead kick a clear chance from close range, despite having room and opportunity to readjust for a simpler attempt that would have tested Vicario.
Barry, too, was unable to influence the game after coming on for the starter in the second half.
It was not for a lack of chance. The majority of Everton's offensive moves came through Grealish and Ndiaye, who tirelessly whipped dangerous crosses into the Tottenham penalty area.
The Toffees: The team head to the Stadium of Light in the top flight on Monday, 3 November at 8 PM.
Spurs: The London club travel to St James' Park on Wednesday, 29 October for their next round Carabao Cup match against the Magpies.
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