The Dutch defender became the initial defender to net two goals in a English top-flight match for Tottenham since the Belgian defender in spring 2013.
Key points
The Spurs defender nods home twice in first half
The home side's Jake O'Brien has goal ruled after video check
Senegalese midfielder nets final goal in 89th minute
The defeat 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 handed the Toffees their initial loss at their new home.
The Toffees were unbeaten in their five previous fixtures at their recently opened stadium at the dockside location, having left Goodison Park behind after 133 years at the conclusion of last season.
But Tottenham's leader Van de Ven struck on two occasions from corners in the opening 45 minutes to place their strong form at risk, and they were unable to turn it around before the midfielder - assisted by former Toffees attacker Richarlison - headed home a final goal to seal the victory.
Jake O'Brien believed he had equalized the tally a short while after the defender's first goal, glancing a powerful header past Guglielmo Vicario from an Everton corner.
Beto, in the meantime, missed a handful of opportunities, while Vicario made a series of fine saves to ensure Tottenham went five away games unbeaten in the English top flight.
But the video assistant referee stepped in, instructing Craig Pawson to check the score on the screen and the official decided that Jack Grealish and the attacker were in an illegal position and had impeded with the Spurs keeper.
This victory elevates the manager's side into third place in the division, a handful of points off local foes and leaders the Gunners.
The Merseyside club stay 14th and sit six points clear of the drop zone.
After a uninspiring weekday performance in the Champions League against Monaco, where they mustered a mere two shots on target, the manager chose the French striker up front instead of former Toffees player the Brazilian.
The new arrival was unable to make much of an impact before being substituted for Richarlison after an hour on the pitch, but it emerged he proved unnecessary in the end.
Defender the Dutchman converted into an offensive threat to be reckoned with.
Spurs' opening strike came from a cleverly executed set-piece play, with the midfielder heading the ball back across the face of goal for an unmarked Van de Ven to head home.
And Ven de Ven - filling in as skipper 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, combining effectively with Kevin Danso as the duo handled superbly with the 34 crosses thrown their way by the opposition.
Everton's new home had been a happy hunting ground, but it appears the freshness may have worn off slightly and fans headed to the exits after the midfielder's final goal for Tottenham.
The end in Everton's winning streak at home will not be a massive worry for the manager, but their attacking woes will be.
Beto and Thierno Barry - the Toffees' pair of established strikers - had scored only a single goal combined before the weekend's match.
And they were failed to add to that miserable tally on a wet and gloomy evening on in Liverpool.
Beto's performance was summed up when he chose to overhead kick a clear chance from near the goal, despite having space and time to reposition for a simpler attempt that would have tested the keeper.
The substitute, too, was unable to make an impact after replacing Beto in the 65th minute.
It was not for a shortage of opportunity. The majority of the home side's offensive moves came through the winger and the forward, who tirelessly delivered dangerous balls into the Tottenham penalty area.
The Toffees: Moyes' men travel to the Stadium of Light in the top flight on Monday, 3 November at 20:00 GMT.
Tottenham: The London club go to Newcastle's ground on late October for their next round League Cup tie against Newcastle.
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