The Dutch defender emerged as the first backline player to net twice in a Premier League game for Tottenham since the Belgian defender in March 2013.
At a glance
The Spurs defender nods into the net twice in first half
The home side's Jake O'Brien has goal ruled after video check
Senegalese midfielder scores third in 89th minute
The defeat is the Merseyside club's initial at their new ground
Micky van de Ven found the net twice as Tottenham prolonged their unbeaten run in away games in the top division and handed Everton their initial loss at their new home.
Everton were undefeated in their last five matches at their new ground at the dockside location, having left Goodison Park behind after 133 years at the conclusion of the previous campaign.
But Spurs captain Van de Ven struck on two occasions from set-pieces in the opening 45 minutes to place their impressive record at jeopardy, and they were failed to mount a comeback before the midfielder - set up by former Toffees attacker the Brazilian - headed home a final goal to seal the victory.
The Everton defender believed he had equalized the scores five minutes after Van de Ven's opener, glancing a powerful header past Guglielmo Vicario from an set-piece.
Beto, in the meantime, failed to convert a number of opportunities, while Vicario made a succession of fine stops to guarantee the London club went five away games unbeaten in the English top flight.
But the VAR intervened, instructing Craig Pawson to check the score on the pitchside monitor and the official ruled that the winger and Iliman Ndiaye were in an illegal position and had impeded with the Tottenham goalkeeper.
This victory elevates Thomas Frank's team into third place in the division, a handful of points off local foes and leaders Arsenal.
Everton stay 14th and are six points clear of the relegation zone.
After a uninspiring weekday display in the European competition against the French side, where they mustered a only attempts on goal, the manager opted for Randal Kolo Muani up front instead of former Toffees player Richarlison.
The summer signing was failed to make much of an impact before being substituted for Richarlison after an hour 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.
Spurs' opening strike came from a well-worked corner routine, with Rodrigo Bentancur heading the ball toward the face of goal for an free Van de Ven to head home.
And Ven de Ven - stepping up as skipper in Cristian Romero's unavailability - notched his second in added time as he outjumped Jordan Pickford to nod in.
Van de Ven was just as impressive in defence, partnering well with his defensive colleague as the pair handled superbly with the 34 crosses thrown their way by Everton.
The club's new home had been a fortress, but it appears the freshness may have faded somewhat and supporters flocked to the gates after Sarr's third for Tottenham.
The end in Everton's winning streak at home will not be a massive worry for David Moyes, but their attacking woes are.
Beto and Thierno Barry - the Everton's two established strikers - had scored just one league goal between them before Sunday's match.
And they were unable to add to that miserable tally on a wet and gloomy evening on Merseyside.
Beto's form was summed up when he chose to overhead kick a golden opportunity from near the goal, even with having room and opportunity to reposition for a simpler attempt that would have challenged Vicario.
The substitute, as well, failed to make an impact after coming on for the starter in the second half.
It was not for a lack of opportunity. Most of Everton's attacks came through Grealish and Ndiaye, who relentlessly whipped threatening balls into the Spurs penalty area.
Everton: Moyes' men travel to Sunderland in the Premier League on early November at 8 PM.
Tottenham: Spurs travel to St James' Park on late October for their fourth-round Carabao Cup tie against the Magpies.
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