The Dutch defender emerged as the initial defender to score twice in a Premier League game for Spurs since the Belgian defender in spring 2013.
At a glance
The Spurs defender heads home two times in opening period
Everton's Jake O'Brien has goal disallowed after video check
Senegalese midfielder nets final goal 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 Spurs extended their unbeaten run in away games in the top division and handed Everton their first defeat at Hill Dickinson Stadium.
The Toffees were unbeaten in their last five matches at their recently opened stadium at Bramley-Moore Dock, having departed Goodison Park behind after 133 years at the end of last season.
But Spurs captain Van de Ven pounced on two occasions from set-pieces in the opening 45 minutes to place their impressive record at jeopardy, and they were unable to turn it around before the midfielder - set up by former Toffees attacker the Brazilian - headed home a third to put the game to bed.
Jake O'Brien believed he had equalized the scores a short while after the defender's first goal, directing a powerful header past Guglielmo Vicario from an set-piece.
Beto, meanwhile, failed to convert a number of chances, while the Italian goalkeeper made a series of fine stops to ensure the London club went five matches on the road unbeaten in the Premier League.
But the VAR stepped in, advising Craig Pawson to check the score on the pitchside monitor and the referee decided that the winger and Iliman Ndiaye were in offside positions and had impeded with the Tottenham goalkeeper.
This victory elevates Thomas Frank's side up to third in the division, five points off local foes and table-toppers Arsenal.
Everton remain in 14th position and are half a dozen points clear of the drop zone.
Following a drab weekday performance in the European competition against Monaco, where they mustered a only two shots on target, Frank chose Randal Kolo Muani in attack instead of ex-Everton forward the Brazilian.
The summer signing was unable to influence the game before being substituted for Richarlison after 60 minutes on the pitch, but it turns out he wasn't needed in the final outcome.
Defender Van de Ven transformed into an attacking force to be reckoned with.
Tottenham's opening strike came from a cleverly executed corner routine, with Rodrigo Bentancur directing the ball toward the six-yard box for an unmarked Van de Ven to head home.
And the captain - filling in as captain in Cristian Romero's unavailability - notched his second in added time as he outjumped Jordan Pickford to head home.
The Dutchman was just as impressive in defence, partnering effectively with Kevin Danso as the pair dealt superbly with the numerous deliveries sent their way by Everton.
Everton's new home had been a fortress, but it seems the freshness may have worn off slightly and fans headed to the exits after the midfielder's final goal for Tottenham.
The end in the team's winning streak at home won't be a major concern for David Moyes, but their striker situation are.
Beto and Thierno Barry - the Everton's two established strikers - had netted just a single goal between them before the weekend's outing.
And they were unable to contribute to that poor tally on a wet and gloomy evening on in Liverpool.
The striker's performance was summed up when he chose to bicycle-kick a clear chance from close range, even with having space and time to readjust for a simpler shot that would have challenged the keeper.
The substitute, too, failed to make an impact after coming on for Beto in the 65th minute.
It wasn't for a shortage of opportunity. The majority of the home side's attacks came through Grealish and Ndiaye, who relentlessly whipped threatening balls into the Tottenham penalty area.
The Toffees: Moyes' men travel to Sunderland in the Premier League on Monday, 3 November at 8 PM.
Tottenham: The London club travel to Newcastle's ground on Wednesday, 29 October for their next round League Cup tie against the Magpies.
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