Micky van de Ven emerged as the initial defender to score twice in a Premier League match for Spurs since the Belgian defender in March 2013.
At a glance
The Spurs defender heads home two times in opening period
Everton's Jake O'Brien has goal disallowed after VAR review
Senegalese midfielder nets final goal in 89th minute
The defeat is Everton's initial at Hill Dickinson Stadium
Micky van de Ven found the net on two occasions as Spurs extended their winning streak on the road in the top division and delivered Everton their initial loss at Hill Dickinson Stadium.
The Toffees were unbeaten in their five previous fixtures at their new ground at Bramley-Moore Dock, having left Goodison Park behind after 133 years at the conclusion of last season.
But Tottenham's leader Van de Ven pounced twice from corners in the opening 45 minutes to put their strong form at jeopardy, and they were unable to turn it around before the midfielder - assisted by ex-Everton forward the Brazilian - headed home a third to seal the victory.
The Everton defender thought he had equalized the scores five minutes after Van de Ven's first goal, glancing a bullet header past Guglielmo Vicario from an set-piece.
The Portuguese striker, in the meantime, failed to convert a handful of opportunities, while the Italian goalkeeper made a series of excellent stops to guarantee Tottenham went five matches on the road without defeat in the Premier League.
But the video assistant referee stepped in, advising Craig Pawson to check the score on the pitchside monitor and the referee ruled that the winger and Iliman Ndiaye were in an illegal position and had interfered with the Spurs keeper.
The win moves Thomas Frank's side up to third in the Premier League, five points off local foes and leaders the Gunners.
The Merseyside club stay in 14th position and sit six points clear of the drop zone.
Following a uninspiring weekday display in the Champions League against Monaco, where they mustered a only two shots on goal, Frank opted for 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 end.
Centre-back the Dutchman transformed into an offensive threat to be reckoned with.
Spurs' opening strike came from a well-worked set-piece play, with Rodrigo Bentancur heading the ball toward the face of goal for an free Van de Ven to head home.
And the captain - stepping up as captain in Cristian Romero's unavailability - added his second in added time as he rose above the England keeper to head home.
The Dutchman was equally impressive in defensive duties, combining effectively with his defensive colleague as the pair handled excellently with the 34 crosses thrown their way by the opposition.
Everton's recent stadium had been a fortress, but it appears the novelty may have faded slightly and fans headed to the gates after the midfielder's final goal for Spurs.
The end in the team's winning streak at home will not be a massive worry for the manager, but their striker situation are.
Beto and Thierno Barry - the Toffees' pair of established centre-forwards - had scored just one league goal combined before Sunday's outing.
And they were unable to contribute to that miserable record on a damp and dreary evening on in Liverpool.
The striker's performance was summed up when he chose to overhead kick a golden opportunity from close range, even with having room and time to reposition for a simpler shot that would have tested the keeper.
The substitute, as well, was unable to influence the game after coming on for the starter in the 65th minute.
It was not for a lack of opportunity. The majority of Everton's offensive moves came through Grealish and the forward, who relentlessly whipped threatening balls into the Tottenham penalty area.
Everton: Moyes' men head to Sunderland in the top flight on early November at 8 PM.
Tottenham: The London club travel to Newcastle's ground on late October for their fourth-round League Cup match against the Magpies.
Emma is a cannabis enthusiast and writer with a passion for exploring the benefits and culture of hemp products.