The Dutch defender became the initial defender to net twice in a Premier League game for Spurs since the Belgian defender in spring 2013.
Match summary
The Spurs defender nods into the net twice in first half
Everton's Jake O'Brien has equalizer ruled after video check
Senegalese midfielder nets third in 89th minute
The defeat is Everton's first at their new ground
The Tottenham defender found the net on two occasions as Spurs extended their winning streak in away games in the top division and delivered the Toffees their first defeat at their new home.
The Toffees were unbeaten in their five previous fixtures at their recently opened stadium at Bramley-Moore Dock, having left Goodison Park behind after more than a century at the conclusion of last season.
But Spurs captain Van de Ven struck on two occasions from corners in the first half to place their strong form at risk, and they were unable to mount a comeback before the midfielder - set up by former Toffees attacker the Brazilian - headed home a third to seal the victory.
The Everton defender believed he had equalized the scores five minutes after the defender's first goal, glancing a powerful header past Guglielmo Vicario from an set-piece.
The Portuguese striker, in the meantime, missed a number of opportunities, while Vicario made a succession of fine saves to ensure the London club went five away games unbeaten in the Premier League.
But the video assistant referee stepped in, advising Craig Pawson to check the goal on the screen and the official decided that the winger and the attacker were in an illegal position and had interfered with the Spurs keeper.
The win moves Thomas Frank's team up to third in the Premier League, a handful of points off local foes and table-toppers the Gunners.
The Merseyside club remain in 14th position and are six points clear of the drop zone.
After a drab midweek display in the Champions League against the French side, where they managed a mere attempts on target, the manager opted for Randal Kolo Muani in attack instead of ex-Everton forward the Brazilian.
The summer signing was unable to influence the game before being replaced for the substitute after 60 minutes on the field, but it emerged he wasn't needed in the final outcome.
Centre-back 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 back across the face of goal for an free Van de Ven to score.
And the captain - filling in as captain in Cristian Romero's unavailability - added his next goal in first-half stoppage time as he rose above the England keeper to head home.
The Dutchman was just as impressive in defence, combining effectively with his defensive colleague as the duo handled excellently with the numerous deliveries sent their way by Everton.
Everton's recent stadium had been a happy hunting ground, but it appears the novelty may have faded slightly and supporters flocked to the gates after the midfielder's third for Spurs.
The end in the team's unbeaten home run will not be a massive worry for the manager, but their striker situation are.
The forward and Thierno Barry - the Toffees' two recognised strikers - had scored just a single goal between them before Sunday's match.
And they were failed to add to that poor record on a damp and dreary night on in Liverpool.
The striker's form was summed up when he opted to bicycle-kick a clear chance from close range, even with having space and time to readjust for a more conventional shot that would have challenged Vicario.
Barry, as well, failed to make an impact 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 the winger and Ndiaye, who tirelessly whipped dangerous balls into the Spurs penalty area.
The Toffees: Moyes' men head to the Stadium of Light in the Premier League on early November at 20:00 GMT.
Spurs: The London club go to Newcastle's ground on late October for their fourth-round League Cup match against Newcastle.
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