The Dutch defender emerged as the first defender to net twice in a Premier League match for Spurs since the Belgian defender in March 2013.
Match summary
The Spurs defender heads home two times in opening period
Everton's Jake O'Brien has equalizer ruled after VAR review
Senegalese midfielder scores third in 89th minute
This loss is Everton's first at Hill Dickinson Stadium
The Tottenham defender found the net on two occasions as Spurs extended their unbeaten run on the road in the Premier League and handed the Toffees their first defeat at their new home.
Everton were unbeaten in their five previous fixtures at their recently opened stadium at Bramley-Moore Dock, having departed Goodison Park behind after 133 years at the end of the previous campaign.
But Spurs captain Van de Ven struck twice from corners in the opening 45 minutes to put their impressive record at risk, and they were unable to mount a comeback before the midfielder - set up by ex-Everton forward Richarlison - nodded in a third to put the game to bed.
The Everton defender believed he had equalized the scores five minutes after Van de Ven's first goal, glancing a bullet header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, meanwhile, failed to convert a number of chances, while Vicario made a series of excellent stops to guarantee the London club went five away games without defeat in the English top flight.
But the VAR intervened, advising Craig Pawson to check the goal on the pitchside monitor and the official decided that Jack Grealish and the attacker were in offside positions and had interfered with the Tottenham goalkeeper.
The win moves the manager's team up to third in the Premier League, five points off local foes and table-toppers the Gunners.
Everton stay 14th and are six points clear of the relegation zone.
Following a uninspiring weekday performance in the European competition against Monaco, where they managed a only two shots on target, the manager chose the French striker in attack instead of former Toffees player Richarlison.
The summer signing was unable to make much of an impact before being replaced for Richarlison after 60 minutes on the field, but it emerged he proved unnecessary in the final outcome.
Defender Van de Ven transformed into an offensive threat to be reckoned with.
Tottenham's opening strike came from a cleverly executed set-piece play, with the midfielder directing the ball toward the face of goal for an free the defender to score.
And the captain - filling in as skipper in the Argentine's unavailability - added his second in first-half stoppage time as he outjumped Jordan Pickford to nod in.
Van de Ven was equally outstanding in defensive duties, combining well with his defensive colleague as the duo dealt excellently with the 34 crosses sent their way by the opposition.
Everton's new home had been a fortress, but it appears the freshness may have faded somewhat and fans headed to the exits after the midfielder's third for Tottenham.
The break in the team's unbeaten home run will not be a massive worry for David Moyes, but their attacking woes will be.
Beto and the other striker - the Everton's pair of established strikers - had netted only one league goal combined before the weekend's match.
And they were failed to contribute to that poor record on a wet and gloomy evening on Merseyside.
Beto's performance was epitomized when he chose to overhead kick a golden opportunity from close range, even with having room and opportunity to reposition for a more conventional shot that would have tested Vicario.
Barry, too, was unable to make an impact after replacing the starter in the second half.
It wasn't for a lack of opportunity. The majority of Everton's attacks came through the winger and the forward, who relentlessly delivered threatening crosses into the Tottenham penalty area.
The Toffees: Moyes' men travel to Sunderland in the Premier League on Monday, 3 November at 8 PM.
Spurs: Spurs travel to St James' Park on late October for their next round Carabao Cup tie against Newcastle.
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Matthew Dean
Matthew Dean
Matthew Dean