Micky van de Ven Double Halts Everton's Run at New Stadium
The Dutch defender emerged as the first defender to net twice in a English top-flight match for Tottenham since Jan Vertonghen in spring 2013.
At a glance
Micky Van de Ven nods into the net twice in first half
The home side's Jake O'Brien has equalizer ruled after video check
Pape Matar Sarr nets final goal in dying moments
The defeat is Everton's initial at their new ground
The Tottenham defender found the net twice as Spurs extended their unbeaten run on the road in the Premier League and handed Everton their initial loss at their new home.
The Toffees were unbeaten in their last five matches at their recently opened stadium at the dockside location, having departed their historic home behind after more than a century at the end of last season.
But Spurs captain the Dutchman pounced on two occasions from set-pieces in the first half to put their strong form at jeopardy, and they were unable to mount a comeback before the midfielder - set up by former Toffees attacker the Brazilian - nodded in a third to seal the victory.
Jake O'Brien thought he had levelled the scores five minutes after Van de Ven's opener, directing a powerful header past the Spurs keeper from an set-piece.
Beto, in the meantime, missed a number of chances, while the Italian goalkeeper made a series of excellent saves to guarantee the London club went five matches on the road unbeaten in the Premier League.
But the VAR stepped in, advising Craig Pawson to review the score on the screen and the referee ruled that the winger and Iliman Ndiaye were in offside positions and had impeded with the Tottenham goalkeeper.
This victory elevates Thomas Frank's side into third place in the division, five points off north London rivals and table-toppers the Gunners.
The Merseyside club remain 14th and are half a dozen points clear of the relegation zone.
Spurs breakdown: The defender excels in role at both ends of the field
Following a drab midweek performance in the Champions League against Monaco, where they managed a only two shots on target, the manager chose Randal Kolo Muani 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 an hour on the field, but it turns out he wasn't needed in the end.
Centre-back the Dutchman transformed into an offensive threat to be reckoned with.
Tottenham's first goal came from a cleverly executed set-piece play, with Rodrigo Bentancur heading the ball toward the face of goal for an unmarked Van de Ven to score.
And Ven de Ven - filling in as skipper in Cristian Romero's absence - notched his second in first-half stoppage time as he rose above the England keeper to head home.
Van de Ven was just as impressive in defensive duties, combining effectively with Kevin Danso as the pair dealt excellently with the numerous deliveries thrown their way by the opposition.
Toffees breakdown: Everton lacking finishing touch
The club's recent stadium had been a happy hunting ground, but it appears the novelty may have worn off slightly and supporters headed to the gates after Sarr's third for Spurs.
The end in the team's unbeaten home run won't be a massive concern for the manager, but their striker situation will be.
Beto and the other striker - the Toffees' pair of established strikers - had netted just a single goal combined before the weekend's outing.
And they were failed to add to that miserable tally on a damp and dreary night on Merseyside.
Beto's performance was summed up when he chose to overhead kick a clear chance from close range, despite having room and opportunity to readjust for a simpler attempt that would have tested Vicario.
Barry, as well, failed to make an impact after replacing the starter in the 65th minute.
It was not for a lack of chance. The majority of Everton's attacks came through Grealish and Ndiaye, who relentlessly whipped dangerous crosses into the Tottenham box.
Upcoming fixtures for both teams?
The Toffees: Moyes' men travel to the Stadium of Light in the top flight on early November at 20:00 GMT.
Spurs: Spurs travel to St James' Park on late October for their next round Carabao Cup tie against the Magpies.