Micky van de Ven Brace Ends Everton's Run at Brand New Home Ground
The Dutch defender became the first defender to score two goals in a Premier League game for Spurs since Jan Vertonghen in spring 2013.
At a glance
The Spurs defender heads home twice in first half
The home side's Jake O'Brien has goal ruled after VAR review
Senegalese midfielder scores final goal in 89th minute
The defeat is Everton's first at Hill Dickinson Stadium
Micky van de Ven found the net twice as Tottenham prolonged their winning streak on the road in the Premier League and handed the Toffees their initial loss at their new home.
The Toffees were undefeated in their five previous fixtures at their recently opened stadium at Bramley-Moore Dock, having departed their historic home behind after 133 years at the conclusion of last season.
But Spurs captain Van de Ven pounced twice from corners 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 Richarlison - nodded in a third to seal the victory.
The Everton defender believed he had equalized the scores a short while after Van de Ven's first goal, directing a powerful header past Guglielmo Vicario from an set-piece.
Beto, meanwhile, failed to convert a handful of chances, while the Italian goalkeeper made a succession of excellent saves to guarantee Tottenham went five away games without defeat in the English top flight.
But the VAR intervened, instructing the match official to check the goal on the pitchside monitor and the referee decided that the winger and the attacker were in offside positions and had impeded with the Tottenham goalkeeper.
The win moves Thomas Frank's side up to third in the division, a handful of points off local foes and leaders Arsenal.
Everton stay 14th and sit six points clear of the drop zone.
Tottenham analysis: The defender fulfils role at each end of pitch
Following a drab weekday performance in the Champions League against the French side, where they mustered a only two shots on target, Frank opted for Randal Kolo Muani in attack instead of ex-Everton forward Richarlison.
The summer signing was failed to make much of an impact before being replaced for Richarlison after 60 minutes on the field, but it emerged he proved unnecessary in the end.
Defender the Dutchman transformed into an offensive threat to be reckoned with.
Spurs' opening strike came from a cleverly executed corner routine, with the midfielder directing the ball back across the six-yard box for an free the defender to head home.
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 Jordan Pickford to head home.
The Dutchman was equally impressive in defensive duties, partnering effectively with his defensive colleague as the duo dealt superbly with the 34 crosses sent their way by the opposition.
Everton analysis: Everton missing striker's instinct
The club's recent stadium had been a happy hunting ground, but it appears the novelty may have faded slightly and supporters headed to the exits after Sarr's third for Spurs.
The end in the team's winning streak at home will not be a major concern for the manager, but their striker situation are.
Beto and Thierno Barry - the Toffees' pair of recognised strikers - had scored only one league goal between them before Sunday's match.
And they were failed to contribute to that poor record on a damp and dreary evening on Merseyside.
Beto's form was summed up when he chose to bicycle-kick a golden opportunity from close range, even with having room and opportunity to readjust for a simpler attempt that would have tested Vicario.
The substitute, as well, was unable to make an impact after coming on for Beto in the second half.
It was not for a lack of chance. The majority of the home side's attacks came through the winger and the forward, who tirelessly whipped threatening crosses into the Spurs box.
Upcoming fixtures for both teams?
Everton: The team head to the Stadium of Light in the top flight 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.