The Dutch defender emerged as the initial backline player to score twice in a English top-flight game for Spurs since the Belgian defender in March 2013.
Match summary
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 Hill Dickinson Stadium
The Tottenham defender scored on two occasions as Tottenham extended their winning streak on the road in the top division and handed the Toffees their first defeat at Hill Dickinson Stadium.
Everton were unbeaten in their five previous fixtures at their new ground at Bramley-Moore Dock, having left Goodison Park behind after more than a century at the conclusion of the previous campaign.
But Spurs captain the Dutchman struck twice from set-pieces in the first half to put their strong form at jeopardy, and they were unable to turn it around before the midfielder - assisted by ex-Everton forward 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 Guglielmo Vicario from an Everton corner.
Beto, meanwhile, failed to convert a handful of chances, while the Italian goalkeeper made a series of fine stops to guarantee Tottenham went five away games unbeaten in the English top flight.
But the video assistant referee stepped in, advising the match official to review the goal on the pitchside monitor and the official decided that Jack Grealish and the attacker were in an illegal position and had interfered with the Tottenham goalkeeper.
The win moves Thomas Frank's team into third place in the Premier League, five points off north London rivals and leaders the Gunners.
Everton stay 14th and sit six points clear of the relegation zone.
After a drab weekday performance in the Champions League against the French side, where they managed a mere attempts on goal, Frank opted for Randal Kolo Muani in attack instead of ex-Everton forward the Brazilian.
The summer signing was failed to influence the game before being substituted for the substitute after an hour on the field, but it turns out he proved unnecessary in the final outcome.
Defender the Dutchman converted into an attacking force to be feared.
Tottenham's opening strike came from a well-worked set-piece play, with the midfielder directing the ball toward the face of goal for an free the defender to head home.
And the captain - filling in as skipper in the Argentine's absence - notched his second in added time as he outjumped Jordan Pickford to head home.
Van de Ven was equally outstanding in defensive duties, combining effectively with his defensive colleague as the pair dealt excellently with the 34 crosses thrown their way by Everton.
Everton's recent stadium had been a happy hunting ground, but it seems the novelty may have worn off somewhat and fans flocked to the gates after the midfielder's third for Tottenham.
The break in Everton's unbeaten home run won't be a major worry for David Moyes, but their striker situation are.
The forward and the other striker - the Toffees' two established strikers - had scored just one league goal between them before the weekend's outing.
And they were unable to add to that poor record on a wet and gloomy night on in Liverpool.
The striker's form was epitomized when he opted to bicycle-kick a golden opportunity from close range, even with having room and time to readjust for a more conventional attempt that would have challenged Vicario.
Barry, as well, was unable to make an impact after replacing Beto in the second half.
It was not for a shortage of opportunity. The majority of Everton's offensive moves came through the winger and Ndiaye, who tirelessly delivered dangerous balls into the Tottenham box.
Everton: Moyes' men travel to the Stadium of Light in the Premier League on Monday, 3 November at 8 PM.
Tottenham: The London club go to St James' Park on late October for their next round League Cup tie against Newcastle.
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