Micky van de Ven Double Ends The Toffees' Run at Brand New Stadium
The Dutch defender became the first defender to net twice in a Premier League game for Spurs since Jan Vertonghen in spring 2013.
Match summary
Micky Van de Ven heads home twice in opening period
The home side's defender has equalizer ruled after VAR review
Senegalese midfielder nets third in dying moments
This loss is Everton's first at their new ground
Micky van de Ven found the net twice as Tottenham extended their unbeaten run in away games in the Premier League and handed Everton their initial loss at their new home.
Everton were undefeated in their five previous fixtures at their new ground at Bramley-Moore Dock, having left their historic home behind after more than a century at the conclusion of the previous campaign.
But Tottenham's leader the Dutchman struck twice from set-pieces in the first half to put their strong form at risk, and they were unable to turn it around before the midfielder - set up by former Toffees attacker Richarlison - nodded in a third to seal the victory.
Jake O'Brien thought he had equalized the tally a short while after Van de Ven's first goal, directing a bullet header past Guglielmo Vicario from an set-piece.
Beto, meanwhile, failed to convert a number of opportunities, while the Italian goalkeeper made a succession of excellent saves to ensure the London club went five matches on the road unbeaten in the English top flight.
But the video assistant referee intervened, instructing Craig Pawson to review the score on the pitchside monitor and the referee ruled that Jack Grealish and the attacker were in an illegal position and had impeded with the Tottenham goalkeeper.
The win moves the manager's team into third place in the Premier League, five points off local foes and leaders Arsenal.
The Merseyside club stay 14th and are half a dozen points clear of the relegation zone.
Tottenham analysis: The defender fulfils duties at each end of the field
After a uninspiring weekday display in the Champions League against Monaco, where they mustered a only two shots on goal, Frank opted for the French striker up front instead of ex-Everton forward the Brazilian.
The new arrival was unable to influence the game before being replaced for the substitute after an hour on the field, but it emerged he proved unnecessary in the end.
Defender the Dutchman transformed into an attacking force to be feared.
Tottenham's opening strike came from a cleverly executed set-piece play, with the midfielder heading the ball toward the six-yard box for an unmarked Van de Ven to score.
And the captain - filling in as captain in the Argentine's unavailability - notched his next goal in first-half stoppage time as he outjumped Jordan Pickford to nod in.
Van de Ven was just as outstanding in defence, partnering effectively with Kevin Danso as the pair dealt excellently with the numerous deliveries sent their way by Everton.
Toffees breakdown: Everton lacking finishing touch
Everton's new home had been a fortress, but it seems the novelty may have worn off somewhat and fans headed to the gates after Sarr's final goal for Spurs.
The break in the team's winning streak at home won't be a massive concern for the manager, but their striker situation are.
The forward and Thierno Barry - the Toffees' pair of recognised strikers - had netted just one league goal between them before the weekend's match.
And they were unable to contribute to that miserable record on a damp and dreary evening on Merseyside.
Beto's performance was summed up when he chose to overhead kick a golden opportunity from close range, even with having space and time to reposition for a more conventional shot that would have tested the keeper.
The substitute, as well, failed to make an impact after replacing the starter in the second half.
It was not for a shortage of chance. Most of Everton's attacks came through the winger and the forward, who tirelessly delivered threatening crosses into the Spurs penalty area.
What next for both teams?
The Toffees: Moyes' men head to Sunderland in the Premier League on Monday, 3 November at 20:00 GMT.
Tottenham: Spurs go to Newcastle's ground on Wednesday, 29 October for their fourth-round League Cup tie against Newcastle.