The Dutch defender emerged as the initial defender to score twice in a Premier League game for Spurs since Jan Vertonghen in March 2013.
At a glance
The Spurs defender heads into the net twice in opening period
The home side's defender has goal ruled after video check
Senegalese midfielder nets third in dying moments
This loss is the Merseyside club's initial at their new ground
The Tottenham defender scored on two occasions as Spurs prolonged their winning streak in away games in the top division and delivered Everton their first defeat at Hill Dickinson Stadium.
Everton were unbeaten in their last five matches at their recently opened stadium at the dockside location, having left their historic home behind after more than a century at the conclusion of last season.
But Tottenham's leader the Dutchman pounced twice from set-pieces in the opening 45 minutes to put their strong form at risk, and they were unable to turn it around before the midfielder - assisted by former Toffees attacker Richarlison - nodded in a final goal to seal the victory.
Jake O'Brien believed he had equalized the tally five minutes after Van de Ven's opener, directing a powerful header past the Spurs keeper from an Everton corner.
The Portuguese striker, in the meantime, missed a number of opportunities, while the Italian goalkeeper made a succession of fine stops to ensure Tottenham went five away games unbeaten in the English top flight.
But the VAR stepped in, advising Craig Pawson to review the goal on the screen and the referee decided that Jack Grealish and the attacker were in an illegal position and had interfered with the Spurs keeper.
This victory elevates Thomas Frank's team into third place in the division, five points off local foes and table-toppers Arsenal.
Everton stay in 14th position and are half a dozen points ahead of the drop zone.
Following a uninspiring weekday performance in the Champions League against Monaco, where they managed a only two shots on target, Frank opted for Randal Kolo Muani up front instead of former Toffees player Richarlison.
The summer signing was failed to make much of an impact before being replaced for Richarlison after an hour on the field, but it turns out he proved unnecessary in the end.
Centre-back the Dutchman transformed into an attacking force to be feared.
Tottenham's first goal came from a cleverly executed set-piece play, with Rodrigo Bentancur heading the ball toward the face of goal for an free the defender to head home.
And the captain - filling in as skipper in Cristian Romero's absence - added his second in added time as he outjumped Jordan Pickford to head home.
The Dutchman was just as outstanding in defensive duties, combining effectively with Kevin Danso as the pair handled superbly with the 34 crosses thrown their way by the opposition.
The club's new home had been a fortress, but it seems the freshness may have worn off somewhat and supporters flocked to the gates after the midfielder's final goal for Tottenham.
The break in Everton's unbeaten home run will not be a massive concern for David Moyes, but their striker situation are.
The forward and Thierno Barry - the Everton's two recognised centre-forwards - had scored only a single goal between them before Sunday's match.
And they were unable to contribute to that poor record on a wet and gloomy evening on Merseyside.
The striker's form was summed up when he chose to overhead kick a golden opportunity from close range, even with having room and time to readjust for a simpler attempt that would have challenged Vicario.
The substitute, too, was unable to influence the game after replacing Beto in the 65th minute.
It was not for a lack of opportunity. Most of Everton's offensive moves came through the winger and the forward, who relentlessly delivered threatening balls into the Tottenham penalty area.
The Toffees: Moyes' men head to the Stadium of Light in the top flight on Monday, 3 November at 20:00 GMT.
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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