Micky van de Ven Double Ends Everton's Run at New Stadium
The Dutch defender became the first defender to net twice in a Premier League match for Tottenham since the Belgian defender in March 2013.
Match summary
The Spurs defender heads into the net twice in opening period
The home side's defender has goal disallowed after video check
Pape Matar Sarr nets third in 89th minute
This loss is Everton's initial at Hill Dickinson Stadium
The Tottenham defender found the net on two occasions as Spurs extended their winning streak in away games in the Premier League and handed the Toffees their first defeat at their new home.
Everton were unbeaten in their five previous fixtures at their new ground at Bramley-Moore Dock, having departed their historic home behind after 133 years at the end of the previous campaign.
But Spurs captain the Dutchman pounced twice from set-pieces in the first half to place their strong form at risk, and they were failed to mount a comeback before Pape Matar Sarr - assisted by former Toffees attacker the Brazilian - nodded in a final goal to seal the victory.
The Everton defender believed he had equalized the scores a short while after Van de Ven's first goal, glancing a powerful header past the Spurs keeper from an Everton corner.
Beto, in the meantime, failed to convert a number of chances, while Vicario made a series of fine stops to ensure the London club went five matches on the road unbeaten in the English top flight.
But the video assistant referee intervened, advising Craig Pawson to review the goal on the pitchside monitor and the referee ruled that Jack Grealish and the attacker were in offside positions and had impeded with the Tottenham goalkeeper.
The win elevates Thomas Frank's side up to third in the Premier League, a handful of points off north London rivals and leaders the Gunners.
Everton remain 14th and are six points clear of the relegation zone.
Tottenham analysis: Van de Ven excels in duties at each end of the field
After a uninspiring midweek performance in the Champions League against Monaco, where they managed a mere attempts on goal, the manager chose Randal Kolo Muani in attack instead of former Toffees player the Brazilian.
The summer signing was unable to make much of an impact before being replaced for Richarlison after an hour on the pitch, but it emerged he proved unnecessary in the final outcome.
Centre-back Van de Ven transformed into an attacking force to be feared.
Tottenham's first goal came from a well-worked set-piece play, with Rodrigo Bentancur heading the ball toward the face of goal for an unmarked the defender to head home.
And Ven de Ven - stepping up as captain in the Argentine's absence - notched his second in first-half stoppage time as he rose above the England keeper to head home.
The Dutchman was just as impressive in defensive duties, combining well with his defensive colleague as the pair handled superbly with the numerous deliveries thrown their way by Everton.
Toffees breakdown: Everton missing finishing touch
The club's recent stadium had been a happy hunting ground, but it appears the novelty may have worn off somewhat and fans flocked to the exits after Sarr's third for Tottenham.
The end in Everton's winning streak at home won't be a major worry for David Moyes, but their attacking woes are.
The forward and the other striker - the Toffees' pair of recognised strikers - had netted only a single goal between them before Sunday's outing.
And they were unable to add to that miserable tally on a wet and gloomy night on Merseyside.
The striker's form was summed up when he opted to bicycle-kick a golden opportunity from close range, even with having room and opportunity to readjust for a more conventional shot that would have challenged Vicario.
The substitute, too, failed to influence the game after replacing Beto in the second half.
It was not for a shortage of opportunity. The majority of Everton's offensive moves came through Grealish and Ndiaye, who tirelessly whipped threatening balls into the Tottenham penalty area.
What next for both teams?
The Toffees: The team head to the Stadium of Light in the Premier League on early November at 20:00 GMT.
Tottenham: Spurs travel to Newcastle's ground on Wednesday, 29 October for their next round Carabao Cup tie against Newcastle.