The Dutch defender became the first backline player to net two goals in a English top-flight match for Tottenham since the Belgian defender in spring 2013.
At a glance
The Spurs defender heads home twice in opening period
The home side's defender has goal ruled after VAR review
Senegalese midfielder nets final goal in 89th minute
This loss is Everton's initial at their new ground
The Tottenham defender scored twice as Tottenham extended their unbeaten run in away games in the top division and handed the Toffees their initial loss at Hill Dickinson Stadium.
The Toffees were undefeated in their last five matches at their new ground at the dockside location, having departed Goodison Park behind after more than a century at the conclusion of last season.
But Tottenham's leader Van de Ven pounced on two occasions from set-pieces in the first half to place their strong form at risk, and they were failed to mount a comeback before the midfielder - assisted by ex-Everton forward the Brazilian - nodded in a final goal to seal the victory.
The Everton defender believed he had levelled the scores a short while after the defender's opener, glancing a bullet header past the Spurs keeper from an set-piece.
The Portuguese striker, in the meantime, failed to convert a handful of chances, while Vicario made a series of fine stops to guarantee Tottenham went five away games without defeat in the English top flight.
But the VAR intervened, advising the match official to review the score on the screen and the referee ruled that Jack Grealish and Iliman Ndiaye were in an illegal position and had impeded with the Tottenham goalkeeper.
This victory moves Thomas Frank's team into third place in the division, a handful of points off north London rivals and table-toppers Arsenal.
Everton remain 14th and are half a dozen points clear of the relegation zone.
After a uninspiring weekday performance in the European competition against Monaco, where they managed a only attempts on target, the manager chose the French striker up front instead of ex-Everton forward Richarlison.
The summer signing was failed to influence the game before being substituted for the substitute after 60 minutes on the pitch, but it emerged he wasn't needed in the final outcome.
Defender the Dutchman converted into an offensive threat to be reckoned with.
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 Van de Ven to head home.
And Ven de Ven - filling in as captain in the Argentine's absence - notched his second in added time as he rose above Jordan Pickford to nod in.
The Dutchman was just as outstanding in defensive duties, combining effectively with Kevin Danso as the duo handled excellently with the numerous deliveries thrown their way by Everton.
The club's new home had been a fortress, but it appears the novelty may have worn off slightly and supporters headed to the gates after the midfielder's third for Tottenham.
The end in the team's unbeaten home run won't be a massive worry for David Moyes, but their striker situation are.
The forward and Thierno Barry - the Toffees' pair of established strikers - had netted only a single goal between them before the weekend's outing.
And they were failed to add to that miserable record on a wet and gloomy night on in Liverpool.
Beto's performance was epitomized when he chose to bicycle-kick a clear chance from close range, even with having room and time to readjust for a simpler attempt that would have tested the keeper.
Barry, too, was unable to influence the game after coming on for the starter in the 65th minute.
It was not for a shortage of chance. Most of the home side's attacks came through Grealish and Ndiaye, who relentlessly whipped dangerous crosses into the Spurs box.
The Toffees: Moyes' men head to the Stadium of Light in the top flight on early November at 8 PM.
Tottenham: Spurs travel to Newcastle's ground on late October for their fourth-round League Cup match against Newcastle.