The Dutch defender became the initial defender to net twice in a Premier League match for Tottenham since Jan Vertonghen in spring 2013.
At a glance
Micky Van de Ven nods home twice in opening period
The home side's Jake O'Brien has goal disallowed after video check
Pape Matar Sarr scores final goal in dying moments
The defeat is Everton's initial at Hill Dickinson Stadium
Micky van de Ven found the net on two occasions as Tottenham prolonged their winning streak in away games in the Premier League and delivered the Toffees their initial loss at their new home.
The Toffees were undefeated in their five previous fixtures at their recently opened stadium at Bramley-Moore Dock, having left Goodison Park behind after 133 years at the end of last season.
But Spurs captain Van de Ven struck twice from set-pieces in the first half to put their strong form at risk, and they were unable to mount a comeback before Pape Matar Sarr - set up 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, directing a powerful header past Guglielmo Vicario from an set-piece.
The Portuguese striker, in the meantime, failed to convert a handful of chances, while Vicario made a succession of excellent stops to ensure Tottenham went five matches on the road without defeat in the English top flight.
But the video assistant referee stepped in, instructing Craig Pawson to review the goal on the screen and the referee decided that the winger and Iliman Ndiaye were in offside positions and had interfered with the Tottenham goalkeeper.
The win elevates the manager's side up to third in the Premier League, five points off local foes and table-toppers Arsenal.
The Merseyside club stay in 14th position and sit six points ahead of the relegation zone.
Following a drab weekday performance in the Champions League against Monaco, where they managed a only two shots on goal, the manager opted for the French striker up front instead of ex-Everton forward Richarlison.
The new arrival was failed to make much of an impact before being substituted for Richarlison after an hour on the pitch, but it emerged he proved unnecessary in the final outcome.
Centre-back Van de Ven converted into an offensive threat to be reckoned with.
Tottenham's opening strike came from a well-worked set-piece play, with Rodrigo Bentancur heading the ball toward the six-yard box for an unmarked Van de Ven to head home.
And Ven de Ven - stepping up as skipper in Cristian Romero's unavailability - added his next goal in first-half stoppage time as he outjumped the England keeper to head home.
Van de Ven was equally outstanding in defensive duties, combining well with his defensive colleague as the duo handled superbly with the numerous deliveries sent their way by the opposition.
Everton's recent stadium had been a fortress, but it seems the freshness may have faded somewhat and supporters headed to the gates after the midfielder's third for Spurs.
The end in Everton's unbeaten home run will not be a massive worry for David Moyes, but their attacking woes are.
The forward and Thierno Barry - the Everton's pair of recognised strikers - had scored just one league goal between them before Sunday's outing.
And they were unable to contribute to that poor record on a wet and gloomy evening on in Liverpool.
Beto's performance was summed up when he opted to bicycle-kick a clear chance from close range, despite having space and time to reposition for a simpler shot that would have challenged the keeper.
The substitute, too, was unable to make an impact after replacing the starter in the 65th minute.
It was not for a shortage of opportunity. Most of the home side's offensive moves came through the winger and the forward, who tirelessly whipped threatening crosses into the Tottenham penalty area.
Everton: Moyes' men travel to the Stadium of Light in the Premier League on Monday, 3 November at 20:00 GMT.
Spurs: Spurs travel to St James' Park on late October for their fourth-round League Cup tie against the Magpies.