The Dutch defender emerged as the first backline player to score twice in a English top-flight game for Tottenham since the Belgian defender in March 2013.
Key points
The Spurs defender nods home two times in first half
The home side's defender has goal ruled after video check
Pape Matar Sarr scores third in dying moments
The defeat is the Merseyside club's first at Hill Dickinson Stadium
Micky van de Ven scored twice as Spurs extended their winning streak in away games in the Premier League and delivered the Toffees their first defeat at their new home.
Everton were unbeaten in their five previous fixtures at their new ground at Bramley-Moore Dock, having left Goodison Park behind after more than a century at the end of last season.
But Tottenham's leader Van de Ven struck twice from set-pieces in the first half to put their impressive record at risk, and they were failed to mount a comeback before Pape Matar Sarr - assisted by former Toffees attacker Richarlison - headed home a final goal to put the game to bed.
The Everton defender believed he had levelled the scores a short while after Van de Ven's first goal, glancing a bullet header past the Spurs keeper from an set-piece.
The Portuguese striker, in the meantime, missed a number of opportunities, while the Italian goalkeeper made a succession of excellent stops to ensure Tottenham went five matches on the road unbeaten in the Premier League.
But the VAR stepped in, advising the match official to review the score on the screen and the official ruled that the winger and the attacker were in offside positions and had interfered with the Tottenham goalkeeper.
This victory moves the manager's team up to third in the Premier League, a handful of points off north London rivals and leaders the Gunners.
Everton stay in 14th position and are half a dozen points ahead of the drop zone.
Following a uninspiring weekday display in the Champions League against the French side, where they mustered a mere attempts on goal, the manager opted for the French striker in attack 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 pitch, but it emerged he proved unnecessary in the final outcome.
Defender the Dutchman transformed into an attacking force to be reckoned with.
Tottenham's opening strike came from a well-worked corner routine, with Rodrigo Bentancur heading the ball back across the face of goal for an free the defender to head home.
And Ven de Ven - filling in as captain in the Argentine's unavailability - added his second in added time as he outjumped Jordan Pickford to head home.
The Dutchman was just as outstanding in defence, combining effectively with his defensive colleague as the duo handled excellently with the numerous deliveries thrown their way by the opposition.
Everton's new home had been a happy hunting ground, but it seems the freshness may have faded slightly and supporters headed to the exits after Sarr's final goal for Spurs.
The end in Everton's winning streak at home won't be a major concern for David Moyes, but their attacking woes are.
The forward and the other striker - the Toffees' pair of established strikers - had scored just one league goal between them before the weekend's match.
And they were failed to add to that poor tally on a damp and dreary evening on in Liverpool.
The striker's performance was epitomized when he chose to overhead kick a golden opportunity from near the goal, even with having space and opportunity to readjust for a more conventional attempt that would have challenged Vicario.
The substitute, as well, failed to influence the game after replacing the starter in the 65th minute.
It was not for a shortage of opportunity. The majority of the home side's attacks came through Grealish and Ndiaye, who relentlessly delivered threatening balls into the Tottenham box.
Everton: The team head to Sunderland in the Premier League on early November at 8 PM.
Tottenham: The London club travel to St James' Park on late October for their fourth-round Carabao Cup match against the Magpies.
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