Micky van de Ven Double Ends Everton's Unbeaten Streak at Brand New Stadium
The Dutch defender became the first backline player to score two goals in a Premier League game for Spurs since Jan Vertonghen in spring 2013.
Match summary
Micky Van de Ven heads into the net two times 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
This loss is Everton's initial at Hill Dickinson Stadium
The Tottenham defender found the net on two occasions as Tottenham prolonged their unbeaten run on the road in the Premier League and delivered Everton their first defeat at their new home.
The Toffees were unbeaten in their last five matches at their new ground at Bramley-Moore Dock, having departed their historic home behind after more than a century at the end of last season.
But Spurs captain the Dutchman struck on two occasions from set-pieces in the first half to place their impressive record at risk, and they were unable to mount a comeback before the midfielder - set up by ex-Everton forward the Brazilian - headed home a final goal to put the game to bed.
Jake O'Brien believed he had equalized the scores five minutes after the defender's first goal, glancing a powerful header past the Spurs keeper from an set-piece.
Beto, meanwhile, missed a handful of opportunities, while Vicario made a series of fine saves to guarantee the London club went five matches on the road unbeaten in the English top flight.
But the video assistant referee stepped in, advising the match official to check the goal on the screen and the official ruled that the winger and Iliman Ndiaye were in an illegal position and had impeded with the Tottenham goalkeeper.
This victory moves Thomas Frank's side up to third in the Premier League, a handful of points off north London rivals and leaders Arsenal.
Everton remain in 14th position and are half a dozen points clear of the drop zone.
Tottenham analysis: Van de Ven excels in duties at both ends of pitch
After a uninspiring weekday performance in the European competition against Monaco, where they mustered a mere two shots on target, Frank chose the French striker up front instead of ex-Everton forward the Brazilian.
The summer signing was failed to make much of an impact before being replaced for Richarlison after 60 minutes on the pitch, but it turns out he wasn't needed in the final outcome.
Defender the Dutchman converted into an attacking force to be feared.
Spurs' first goal came from a well-worked corner routine, with Rodrigo Bentancur heading the ball back across the face of goal for an free the defender to score.
And the captain - stepping up as captain in the Argentine's unavailability - notched his next goal in first-half stoppage time as he rose above Jordan Pickford to nod in.
Van de Ven was equally outstanding in defensive duties, partnering well with his defensive colleague as the pair handled superbly with the 34 crosses sent their way by Everton.
Toffees breakdown: Toffees lacking finishing touch
Everton's recent stadium had been a fortress, but it seems the novelty may have worn off slightly and supporters flocked to the exits after the midfielder's third for Spurs.
The end in the team's unbeaten home run will not be a major worry for David Moyes, but their attacking woes will be.
The forward and the other striker - the Toffees' two recognised strikers - had scored only a single goal combined before Sunday's match.
And they were unable to contribute to that poor record on a damp and dreary evening on in Liverpool.
Beto's performance was epitomized when he chose to bicycle-kick a clear chance from close range, despite having space and opportunity to reposition for a more conventional shot that would have challenged the keeper.
Barry, too, failed to make an impact after replacing Beto in the 65th minute.
It was not for a shortage of chance. Most of Everton's attacks came through Grealish and the forward, who tirelessly delivered threatening crosses into the Tottenham box.
Upcoming fixtures for these two sides?
Everton: Moyes' men travel to the Stadium of Light in the top flight on early November at 20:00 GMT.
Tottenham: The London club travel to Newcastle's ground on Wednesday, 29 October for their next round Carabao Cup tie against the Magpies.