The Dutch defender became the first defender to net two goals in a Premier League game for Tottenham since Jan Vertonghen in spring 2013.
At a glance
Micky Van de Ven heads home two times in first half
The home side's defender has equalizer disallowed after video check
Senegalese midfielder nets third in dying moments
The defeat is Everton's initial at their new ground
The Tottenham defender scored twice as Tottenham prolonged their winning streak in away games in the top division and handed Everton their first defeat at Hill Dickinson Stadium.
The Toffees were undefeated in their last five matches at their recently opened stadium at the dockside location, having left their historic home behind after more than a century at the conclusion of the previous campaign.
But Spurs captain the Dutchman pounced twice from corners in the first half to put their impressive record at risk, and they were unable to turn it around before the midfielder - set up by former Toffees attacker Richarlison - nodded in a final goal to seal the victory.
The Everton defender thought he had equalized the tally a short while after Van de Ven's first goal, directing a powerful header past the Spurs keeper from an Everton corner.
Beto, in the meantime, missed a handful of chances, while the Italian goalkeeper made a succession of fine stops to ensure the London club went five matches on the road without defeat in the Premier League.
But the VAR intervened, instructing the match official to review the score on the pitchside monitor and the official decided that the winger and Iliman Ndiaye were in an illegal position and had interfered with the Tottenham goalkeeper.
This victory moves Thomas Frank's team up to third in the division, five points off north London rivals and leaders Arsenal.
The Merseyside club remain 14th and are half a dozen points ahead of the relegation zone.
Following a uninspiring midweek display in the European competition against the French side, where they managed a only attempts on target, the manager chose the French striker up front instead of former Toffees player Richarlison.
The new arrival was unable to influence the game before being substituted for the substitute after an hour on the pitch, but it emerged he wasn't needed in the end.
Defender the Dutchman transformed into an attacking force to be feared.
Spurs' opening strike came from a well-worked corner routine, with Rodrigo Bentancur heading the ball back across the six-yard box for an free Van de Ven to head home.
And Ven de Ven - stepping up as skipper in the Argentine's absence - added his second in added time as he rose above the England keeper to head home.
Van de Ven was equally impressive in defence, combining effectively with his defensive colleague as the pair handled excellently with the numerous deliveries thrown their way by Everton.
Everton's new home had been a happy hunting ground, but it seems the freshness may have worn off slightly and supporters flocked to the exits after Sarr's third for Spurs.
The end in Everton's unbeaten home run won't be a massive worry for the manager, but their attacking woes will be.
The forward and the other striker - the Everton's pair of established centre-forwards - had netted just one league goal between them before Sunday's outing.
And they were unable to contribute to that miserable record on a wet and gloomy evening on Merseyside.
The striker's form was epitomized when he chose to bicycle-kick a clear chance from near the goal, despite having space and time to reposition for a simpler attempt that would have tested the keeper.
The substitute, too, was unable to influence the game after coming on for Beto in the 65th minute.
It wasn't for a lack of opportunity. Most of Everton's attacks came through the winger and Ndiaye, who tirelessly whipped threatening balls into the Spurs box.
The Toffees: The team head to Sunderland in the top flight on early November at 20:00 GMT.
Spurs: The London club go to Newcastle's ground on late October for their fourth-round League Cup match against the Magpies.
Maya is a wellness coach and writer passionate about holistic health, sharing practical tips for balanced living in the UK.