Micky van de Ven emerged as the initial defender to score two goals in a English top-flight game for Spurs since Jan Vertonghen in spring 2013.
Match summary
Micky Van de Ven nods home two times in first half
Everton's Jake O'Brien has goal disallowed after VAR review
Senegalese midfielder nets final goal in dying moments
The defeat is the Merseyside club's initial at their new ground
The Tottenham defender scored twice as Spurs extended their unbeaten run on the road in the Premier League and handed Everton their initial loss at their new home.
Everton were unbeaten in their last five matches at their recently opened stadium at Bramley-Moore Dock, having departed Goodison Park behind after more than a century at the conclusion of last season.
But Tottenham's leader the Dutchman pounced twice from corners in the opening 45 minutes to place their impressive record at risk, and they were failed to mount a comeback before Pape Matar Sarr - assisted by former Toffees attacker the Brazilian - nodded in a third to put the game to bed.
The Everton defender thought he had equalized the scores a short while after the defender's opener, directing a bullet header past Guglielmo Vicario from an Everton corner.
Beto, in the meantime, failed to convert a number of opportunities, while Vicario made a series of excellent stops to guarantee Tottenham went five matches on the road unbeaten in the Premier League.
But the video assistant referee stepped in, instructing Craig Pawson 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 Spurs keeper.
This victory elevates Thomas Frank's team into third place in the division, five points off local foes and leaders the Gunners.
The Merseyside club stay 14th and are half a dozen points ahead of the drop zone.
After a uninspiring midweek performance in the Champions League against Monaco, where they managed a mere two shots on target, the manager chose the French striker up front instead of ex-Everton forward Richarlison.
The new arrival was failed to make much of an impact before being substituted for Richarlison after an hour on the field, but it emerged he wasn't needed in the final outcome.
Centre-back the Dutchman converted into an attacking force to be feared.
Spurs' opening strike came from a well-worked corner routine, with Rodrigo Bentancur heading the ball toward the face of goal for an free the defender to score.
And the captain - filling in as captain 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, combining well with his defensive colleague as the duo handled excellently with the 34 crosses thrown their way by the opposition.
The club's new home had been a happy hunting ground, but it seems the freshness may have worn off slightly and fans flocked to the exits after the midfielder's final goal for Spurs.
The end in Everton's winning streak at home will not be a major worry for David Moyes, but their attacking woes are.
Beto and Thierno Barry - the Everton's two established centre-forwards - had netted only a single goal combined before Sunday's match.
And they were unable to contribute to that miserable tally on a damp and dreary evening on Merseyside.
The striker's performance was summed up when he chose to overhead kick a clear chance from close range, despite having space and opportunity to reposition for a simpler attempt that would have tested the keeper.
Barry, too, was unable to influence the game after coming on for Beto in the 65th minute.
It wasn't for a lack of chance. The majority of Everton's attacks came through the winger and the forward, who tirelessly whipped dangerous crosses into the Tottenham box.
The Toffees: Moyes' men travel to the Stadium of Light in the top flight on early November at 8 PM.
Spurs: The London club go to Newcastle's ground on late October for their next round Carabao Cup match against the Magpies.
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