The Dutch defender emerged as the initial defender to net two goals in a Premier League game for Tottenham since Jan Vertonghen in spring 2013.
Key points
The Spurs defender heads into the net twice in first half
Everton's defender has goal ruled after video check
Senegalese midfielder scores third in dying moments
This loss is the Merseyside club's first at Hill Dickinson Stadium
The Tottenham defender found the net on two occasions as Spurs extended their winning streak on the road in the top division and handed the Toffees their initial loss at their new home.
The Toffees were unbeaten in their five previous fixtures at their new ground at the dockside location, having departed Goodison Park behind after 133 years at the end of last season.
But Spurs captain the Dutchman struck twice from corners in the opening 45 minutes to place their strong form at jeopardy, and they were unable to mount a comeback before Pape Matar Sarr - assisted by ex-Everton forward Richarlison - nodded in a third to seal the victory.
Jake O'Brien believed he had equalized the scores a short while after Van de Ven's first goal, glancing a powerful header past the Spurs keeper from an set-piece.
Beto, meanwhile, missed a number of opportunities, while the Italian goalkeeper made a series of fine stops to guarantee Tottenham went five away games without defeat in the English top flight.
But the video assistant referee intervened, advising Craig Pawson to check the score on the pitchside monitor and the referee decided that Jack Grealish and the attacker were in offside positions and had interfered with the Tottenham goalkeeper.
The win elevates the manager's team into third place in the division, five points off north London rivals and leaders Arsenal.
Everton stay in 14th position and are six points ahead of the drop zone.
After a uninspiring midweek performance in the Champions League against the French side, where they managed a only two shots on goal, the manager chose Randal Kolo Muani in attack instead of ex-Everton forward Richarlison.
The new arrival was failed to make much of an impact before being replaced for Richarlison after an hour on the field, but it turns out he wasn't needed in the end.
Centre-back the Dutchman converted into an attacking force to be reckoned with.
Tottenham's opening strike came from a cleverly executed corner routine, with Rodrigo Bentancur heading the ball toward the face of goal for an unmarked the defender to head home.
And Ven de Ven - stepping up as skipper in the Argentine's unavailability - notched his next goal in added time as he rose above Jordan Pickford to nod in.
Van de Ven was just as impressive in defensive duties, combining effectively with Kevin Danso as the pair handled superbly with the 34 crosses thrown their way by Everton.
Everton's new home had been a fortress, but it appears the freshness may have worn off somewhat and fans flocked to the exits after the midfielder's final goal for Tottenham.
The break in Everton's winning streak at home won't be a major worry for the manager, but their striker situation will be.
The forward and Thierno Barry - the Everton's two established centre-forwards - had scored just one league goal between them before Sunday's match.
And they were failed to contribute to that miserable record on a damp and dreary night on in Liverpool.
The striker's form was summed up when he opted to bicycle-kick a golden opportunity from close range, despite having room and opportunity to reposition for a simpler shot that would have tested the keeper.
Barry, as well, was unable to influence the game after coming on for Beto in the 65th minute.
It wasn't for a shortage of opportunity. Most of Everton's offensive moves came through the winger and the forward, who tirelessly delivered threatening balls into the Tottenham box.
Everton: Moyes' men head to Sunderland in the Premier League on Monday, 3 November at 20:00 GMT.
Spurs: Spurs go to St James' Park on late October for their fourth-round Carabao Cup tie against Newcastle.
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Lori Wilson
Lori Wilson
Lori Wilson
Lori Wilson
Lori Wilson