The Dutch defender emerged as the initial backline player to net two goals in a English top-flight match for Spurs since the Belgian defender in March 2013.
Key points
Micky Van de Ven nods home twice in first half
The home side's Jake O'Brien has equalizer disallowed after VAR review
Senegalese midfielder scores third in 89th minute
The defeat is the Merseyside club's initial at Hill Dickinson Stadium
The Tottenham defender found the net twice as Tottenham extended their unbeaten run on the road in the top division and handed Everton their initial loss at Hill Dickinson Stadium.
The Toffees were undefeated in their last five matches at their new ground 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 pounced twice from set-pieces in the first half to place their strong form at jeopardy, and they were failed to mount a comeback before Pape Matar Sarr - set up by ex-Everton forward Richarlison - nodded in a final goal to put the game to bed.
The Everton defender believed he had equalized the scores five minutes after the defender's first goal, directing a powerful header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, meanwhile, failed to convert a handful of chances, while the Italian goalkeeper made a series of fine stops to ensure Tottenham went five away games without defeat in the English top flight.
But the video assistant referee stepped in, advising the match official to review the goal on the screen and the referee decided that Jack Grealish and the attacker were in an illegal position and had impeded with the Tottenham goalkeeper.
The win elevates the manager's team up to third in the division, a handful of points off north London rivals and leaders the Gunners.
Everton remain 14th and sit half a dozen points ahead of the relegation zone.
After a drab midweek performance in the European competition against the French side, where they managed a mere two shots on target, Frank opted for the French striker up front instead of former Toffees player the Brazilian.
The new arrival was failed to make much of an impact before being replaced for Richarlison after 60 minutes on the pitch, but it turns out he wasn't needed in the final outcome.
Centre-back Van de Ven converted into an attacking force to be reckoned with.
Tottenham's opening strike came from a cleverly executed corner routine, with the midfielder heading the ball toward the six-yard box for an unmarked Van de Ven to score.
And Ven de Ven - stepping up as skipper in the Argentine's unavailability - notched his second in first-half stoppage time as he rose above Jordan Pickford to head home.
The Dutchman was equally impressive in defence, partnering well with Kevin Danso as the duo dealt superbly with the numerous deliveries sent their way by Everton.
The club's recent stadium had been a fortress, but it seems the novelty may have worn off slightly and fans flocked to the gates after the midfielder's third for Spurs.
The break in the team's unbeaten home run won't be a major worry for David Moyes, but their striker situation will be.
The forward and Thierno Barry - the Toffees' pair of established centre-forwards - had scored just a single goal between them before Sunday's outing.
And they were failed to add to that miserable record on a damp and dreary evening on Merseyside.
Beto's form was summed up when he opted to bicycle-kick a golden opportunity from close range, despite having space and time to readjust for a simpler shot that would have challenged the keeper.
The substitute, too, was unable to make an impact after coming on for the starter in the second half.
It was not for a lack of opportunity. Most of the home side's offensive moves came through the winger and the forward, who tirelessly whipped dangerous balls into the Spurs penalty area.
The Toffees: Moyes' men travel to Sunderland in the Premier League on Monday, 3 November at 8 PM.
Spurs: The London club go to St James' Park on Wednesday, 29 October for their next round League Cup tie against Newcastle.
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