Micky van de Ven became the initial 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 into the net twice in opening period
The home side's Jake O'Brien has equalizer ruled after video check
Pape Matar Sarr scores third in 89th minute
The defeat is the Merseyside club's first at their new ground
The Tottenham defender scored twice as Tottenham extended their winning streak on the road in the Premier League and handed the Toffees their first defeat at Hill Dickinson Stadium.
The Toffees were undefeated in their last five matches at their new ground at Bramley-Moore Dock, having departed Goodison Park behind after 133 years at the end of the previous campaign.
But Spurs captain Van de Ven struck on two occasions from set-pieces in the first half to place their impressive record at risk, and they were unable to turn it around before the midfielder - set up by former Toffees attacker the Brazilian - headed home a final goal to seal the victory.
Jake O'Brien thought he had equalized the tally five minutes after Van de Ven's first goal, glancing a bullet header past Guglielmo Vicario from an Everton corner.
Beto, meanwhile, missed a handful of chances, while the Italian goalkeeper made a succession of excellent stops to ensure the London club went five away games without defeat in the Premier League.
But the VAR stepped in, instructing the match official to check the goal on the screen and the official decided that the winger and the attacker were in offside positions and had impeded with the Spurs keeper.
The win elevates the manager's side into third place in the division, a handful of points off north London rivals and leaders the Gunners.
The Merseyside club stay in 14th position and sit half a dozen points ahead of the relegation zone.
After a uninspiring weekday display in the Champions League against Monaco, where they mustered a only two shots on goal, the manager chose Randal Kolo Muani up front instead of ex-Everton forward Richarlison.
The new arrival was unable 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 final outcome.
Defender Van de Ven transformed into an attacking force to be reckoned with.
Tottenham's first goal came from a well-worked set-piece play, with Rodrigo Bentancur heading the ball toward the six-yard box for an unmarked the defender to score.
And Ven de Ven - stepping up as captain in Cristian Romero's absence - notched his second in first-half stoppage time as he outjumped Jordan Pickford to head home.
Van de Ven was equally impressive in defence, partnering effectively with Kevin Danso as the pair handled superbly with the 34 crosses sent their way by Everton.
Everton's recent stadium had been a happy hunting ground, but it appears the freshness may have faded slightly and fans headed to the gates after Sarr's final goal for Spurs.
The break in Everton's unbeaten home run won't be a massive concern for the manager, but their striker situation are.
The forward and the other striker - the Toffees' pair of established centre-forwards - had netted just a single goal combined before Sunday's outing.
And they were unable to contribute to that poor tally on a damp and dreary night on in Liverpool.
The striker's form was summed up when he chose to bicycle-kick a golden opportunity from close range, even with having room and time to readjust for a more conventional shot that would have tested the keeper.
The substitute, too, was unable to make an impact after replacing the starter in the 65th minute.
It wasn't for a lack of chance. The majority of the home side's offensive moves came through the winger and Ndiaye, who relentlessly whipped dangerous crosses into the Spurs penalty area.
The Toffees: The team head to the Stadium of Light in the Premier League on Monday, 3 November at 8 PM.
Spurs: The London club travel to Newcastle's ground on Wednesday, 29 October for their next round League Cup match against the Magpies.
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