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 spring 2013.
Key points
Micky Van de Ven heads into the net twice in opening period
The home side's defender has goal disallowed after VAR review
Senegalese midfielder scores third in 89th minute
This loss is the Merseyside club's initial at Hill Dickinson Stadium
Micky van de Ven found the net on two occasions as Tottenham prolonged their unbeaten run on the road in the top division and delivered Everton their initial loss at their new home.
Everton were unbeaten in their five previous fixtures at their recently opened stadium at Bramley-Moore Dock, having departed Goodison Park behind after 133 years at the conclusion of the previous campaign.
But Tottenham's leader the Dutchman struck on two occasions from set-pieces in the first half to place their strong form at jeopardy, and they were failed to mount a comeback before Pape Matar Sarr - set up by former Toffees attacker Richarlison - headed home a final goal to seal the victory.
Jake O'Brien believed he had equalized the scores a short while after the defender's first goal, glancing a bullet header past Guglielmo Vicario from an set-piece.
Beto, in the meantime, failed to convert a number of chances, while Vicario made a series of excellent stops to guarantee the London club went five away games unbeaten in the Premier League.
But the VAR stepped in, instructing Craig Pawson to check the goal on the screen and the referee decided that the winger and the attacker were in offside positions and had interfered with the Tottenham goalkeeper.
The win elevates the manager's team into third place in the Premier League, five points off north London rivals and leaders Arsenal.
Everton remain 14th and sit half a dozen points clear of the relegation zone.
Following a uninspiring weekday performance in the European competition against Monaco, where they mustered a only two shots on target, the manager opted for the French striker up front instead of former Toffees player Richarlison.
The summer signing was unable to influence the game before being substituted for the substitute after an hour on the pitch, but it emerged he proved unnecessary in the end.
Defender Van de Ven transformed into an offensive threat to be feared.
Tottenham's first goal came from a cleverly executed corner routine, with the midfielder heading the ball toward the six-yard box for an free Van de Ven to head home.
And the captain - filling in as captain in Cristian Romero's absence - added his second in first-half stoppage time as he rose above Jordan Pickford to nod in.
The Dutchman was equally outstanding in defensive duties, combining effectively with his defensive colleague as the pair handled excellently with the 34 crosses thrown their way by Everton.
Everton's recent stadium had been a fortress, but it appears the freshness may have faded slightly and fans flocked to the gates after the midfielder's third for Spurs.
The break 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 Everton's pair of established strikers - had scored only a single goal between them before Sunday's outing.
And they were unable to add to that miserable record on a damp and dreary evening on in Liverpool.
Beto's performance was summed up when he opted to bicycle-kick a clear chance from near the goal, even with having room and opportunity to readjust for a simpler shot that would have challenged Vicario.
The substitute, too, failed to influence the game after replacing Beto in the second half.
It was not for a shortage of chance. Most of Everton's offensive moves came through the winger and Ndiaye, who relentlessly delivered dangerous balls into the Tottenham penalty area.
The Toffees: Moyes' men travel to the Stadium of Light in the Premier League on early November at 8 PM.
Tottenham: The London club travel to Newcastle's ground on late October for their fourth-round League Cup tie against the Magpies.
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