The Dutch defender emerged as the initial defender to net twice in a English top-flight game for Tottenham since the Belgian defender in March 2013.
At a glance
Micky Van de Ven nods into the net two times in first half
The home side's defender has goal ruled after VAR review
Pape Matar Sarr nets third in dying moments
The defeat is Everton's initial at their new ground
The Tottenham defender found the net twice as Tottenham extended their winning streak in away games in the Premier League and handed the Toffees their initial loss at Hill Dickinson Stadium.
The Toffees were unbeaten in their last five matches at their new ground at Bramley-Moore Dock, having left their historic home behind after more than a century at the end of last season.
But Tottenham's leader Van de Ven struck on two occasions from set-pieces in the opening 45 minutes to place their impressive record at risk, and they were failed to mount a comeback before the midfielder - assisted by ex-Everton forward Richarlison - headed home a final goal to seal the victory.
The Everton defender thought he had equalized the scores five minutes after the defender's opener, directing a powerful header past Guglielmo Vicario from an set-piece.
The Portuguese striker, meanwhile, failed to convert a handful of opportunities, while Vicario made a succession of fine saves to guarantee Tottenham went five away games without defeat in the Premier League.
But the VAR stepped in, advising Craig Pawson to check the goal on the screen and the official decided that the winger and Iliman Ndiaye were in offside positions and had interfered with the Spurs keeper.
The win moves Thomas Frank's side up to third in the Premier League, a handful of points off local foes and table-toppers Arsenal.
Everton stay 14th and are six points clear of the drop zone.
Following a uninspiring midweek performance in the Champions League against Monaco, where they managed a mere two shots on goal, Frank opted for Randal Kolo Muani up front instead of ex-Everton forward the Brazilian.
The summer signing was failed to make much of an impact before being replaced for the substitute after 60 minutes on the pitch, but it turns out he wasn't needed in the final outcome.
Defender Van de Ven transformed into an offensive threat to be reckoned with.
Tottenham's first goal came from a well-worked set-piece play, with the midfielder heading the ball back across the six-yard box for an unmarked Van de Ven to score.
And Ven de Ven - stepping up as captain in the Argentine's unavailability - added his second in first-half stoppage time as he outjumped Jordan Pickford to head home.
Van de Ven was just as outstanding in defence, partnering effectively with Kevin Danso as the pair dealt superbly with the numerous deliveries sent their way by the opposition.
Everton's new home had been a happy hunting ground, but it appears the freshness may have worn off somewhat and fans flocked to the exits after Sarr's final goal for Spurs.
The end in the team's unbeaten home run will not be a major concern for David Moyes, but their attacking woes are.
Beto and the other striker - the Toffees' pair of established centre-forwards - had netted only a single goal combined before Sunday's match.
And they were unable to add to that poor record on a wet and gloomy night on Merseyside.
The striker's form was summed up when he opted to overhead kick a golden opportunity from near the goal, even with having room and opportunity to reposition for a more conventional shot that would have challenged the keeper.
The substitute, too, was unable to make an impact after replacing Beto in the 65th minute.
It was not for a shortage of chance. Most of Everton's attacks came through Grealish and the forward, who tirelessly whipped dangerous crosses into the Spurs penalty area.
Everton: The team travel to the Stadium of Light in the Premier League on early November at 20:00 GMT.
Spurs: The London club go to St James' Park on late October for their next round League Cup tie against the Magpies.
Elena Marchetti is a technology journalist with a passion for demystifying complex topics. She has been covering tech trends for over a decade.