The Dutch defender emerged as the first defender to score two goals in a English top-flight game for Spurs since Jan Vertonghen in March 2013.
Key points
Micky Van de Ven heads into the net two times in first half
Everton's Jake O'Brien has equalizer ruled after VAR review
Pape Matar Sarr scores third in dying moments
This loss is the Merseyside club's initial at Hill Dickinson Stadium
The Tottenham defender found the net twice as Spurs prolonged their unbeaten run in away games in the Premier League 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 the dockside location, having left their historic home behind after 133 years at the end of the previous campaign.
But Spurs captain Van de Ven pounced twice from set-pieces in the opening 45 minutes to place their strong form at jeopardy, and they were unable to mount a comeback before the midfielder - set up by ex-Everton forward the Brazilian - headed home a third to put the game to bed.
Jake O'Brien believed he had equalized the scores a short while after the defender's opener, glancing a bullet header past the Spurs keeper from an set-piece.
Beto, in the meantime, failed to convert a handful of chances, while the Italian goalkeeper made a succession of fine saves to guarantee Tottenham went five matches on the road unbeaten in the Premier League.
But the VAR stepped in, advising the match official to review the score on the screen and the referee decided that the winger and Iliman Ndiaye were in an illegal position and had impeded with the Tottenham goalkeeper.
This victory moves Thomas Frank's team into third place in the Premier League, five points off local foes and table-toppers Arsenal.
The Merseyside club stay 14th and sit six points clear of the relegation zone.
Following a uninspiring midweek display in the Champions League against the French side, where they mustered a only attempts on goal, the manager opted for Randal Kolo Muani in attack instead of former Toffees player the Brazilian.
The summer signing was unable to make much of an impact before being replaced for Richarlison after 60 minutes on the field, but it turns out he wasn't needed in the end.
Defender Van de Ven converted into an attacking force to be reckoned with.
Tottenham's opening strike came from a well-worked corner routine, with the midfielder heading the ball toward the six-yard box for an free the defender to score.
And Ven de Ven - filling in as captain in the Argentine's absence - notched his next goal in added time as he outjumped the England keeper to head home.
The Dutchman was just as outstanding in defensive duties, partnering well with Kevin Danso as the duo handled superbly with the numerous deliveries sent their way by the opposition.
The club's new home had been a fortress, but it seems the freshness may have worn off somewhat and fans flocked to the exits after the midfielder's third for Tottenham.
The end in the team's winning streak at home will not be a massive concern for David Moyes, but their striker situation will be.
The forward and Thierno Barry - the Everton's two established centre-forwards - had scored only a single goal between them before the weekend's outing.
And they were failed to add to that poor tally on a damp and dreary night on in Liverpool.
Beto's form was epitomized when he chose to overhead kick a clear chance from close range, even with having room and opportunity to readjust for a more conventional shot that would have tested Vicario.
The substitute, too, failed to influence the game after coming on for Beto in the 65th minute.
It wasn't for a shortage of chance. The majority of the home side's attacks came through the winger and Ndiaye, who tirelessly delivered threatening crosses into the Tottenham penalty area.
The Toffees: The team travel to the Stadium of Light in the top flight on Monday, 3 November at 8 PM.
Spurs: The London club travel to Newcastle's ground on Wednesday, 29 October for their fourth-round Carabao Cup match against Newcastle.