The Dutch defender emerged as the first defender to score twice in a English top-flight game for Spurs since the Belgian defender in spring 2013.
Key points
Micky Van de Ven nods home twice in opening period
The home side's Jake O'Brien has equalizer ruled after video check
Pape Matar Sarr scores third in 89th minute
The defeat is the Merseyside club's first at their new ground
Micky van de Ven found the net twice as Spurs extended their unbeaten run on the road in the Premier League and delivered the Toffees their first defeat at their new home.
Everton were undefeated in their five previous fixtures at their new ground at Bramley-Moore Dock, having left their historic home behind after 133 years at the end of last season.
But Tottenham's leader Van de Ven pounced twice from corners in the first half to place their strong form at risk, and they were unable to turn it around before Pape Matar Sarr - assisted by former Toffees attacker the Brazilian - nodded in a third to seal the victory.
Jake O'Brien believed he had equalized the scores five minutes after Van de Ven's opener, directing a powerful header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, in the meantime, missed a handful of opportunities, while Vicario made a succession of fine saves to guarantee the London club went five away games unbeaten in the English top flight.
But the VAR stepped in, instructing Craig Pawson to review the score on the screen and the referee ruled that the winger and Iliman Ndiaye were in offside positions and had interfered with the Tottenham goalkeeper.
This victory moves the manager's side up to third in the Premier League, a handful of points off north London rivals and table-toppers the Gunners.
Everton stay in 14th position and sit six points clear of the drop zone.
Following a uninspiring weekday display in the Champions League against the French side, where they mustered a only two shots on goal, the manager chose the French striker up front instead of ex-Everton forward the Brazilian.
The summer signing was unable to influence the game before being replaced for the substitute after 60 minutes on the field, but it turns out he wasn't needed in the end.
Centre-back Van de Ven converted into an offensive threat to be feared.
Spurs' first goal came from a well-worked corner routine, with Rodrigo Bentancur heading the ball toward the six-yard box for an unmarked the defender to head home.
And Ven de Ven - filling in as captain in Cristian Romero's absence - added his next goal in first-half stoppage time as he outjumped the England keeper to nod in.
The Dutchman was equally impressive in defence, partnering well with Kevin Danso as the duo handled excellently with the 34 crosses sent their way by Everton.
The club's new home had been a fortress, but it appears the novelty may have faded slightly and fans flocked to the gates after the midfielder's final goal for Spurs.
The break in Everton's unbeaten home run will not be a massive worry for David Moyes, but their striker situation will be.
The forward and Thierno Barry - the Everton's two recognised centre-forwards - had scored just a single goal between them before the weekend's outing.
And they were failed to contribute to that poor tally on a damp and dreary evening on in Liverpool.
The striker's performance was summed up when he opted to overhead kick a clear chance from near the goal, despite having space and opportunity to reposition for a more conventional shot that would have challenged the keeper.
The substitute, as well, failed to influence the game after coming on for the starter in the second half.
It wasn't for a lack of chance. Most of Everton's attacks came through Grealish and the forward, who relentlessly delivered dangerous crosses into the Tottenham penalty area.
The Toffees: Moyes' men travel to Sunderland in the Premier League on early November at 20:00 GMT.
Spurs: The London club travel to Newcastle's ground on Wednesday, 29 October for their next round Carabao Cup match against Newcastle.
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