Micky van de Ven emerged as the first backline player to score two goals in a English top-flight game for Tottenham since the Belgian defender in spring 2013.
At a glance
The Spurs defender heads home twice in first half
The home side's defender has equalizer ruled after VAR review
Senegalese midfielder scores third in 89th minute
The defeat is Everton's initial at their new ground
The Tottenham defender found the net on two occasions as Tottenham prolonged their unbeaten run on the road in the Premier League and delivered Everton their first defeat at their new home.
Everton were undefeated in their five previous fixtures at their recently opened stadium at the dockside location, having left Goodison Park behind after 133 years at the end of the previous campaign.
But Spurs captain Van de Ven pounced on two occasions from set-pieces in the opening 45 minutes to place their impressive record at risk, and they were unable to mount a comeback before the midfielder - assisted by ex-Everton forward the Brazilian - headed home a third to seal the victory.
The Everton defender thought he had levelled the scores a short while after Van de Ven's first goal, directing a bullet header past Guglielmo Vicario from an set-piece.
The Portuguese striker, meanwhile, missed a handful of chances, while Vicario made a series of fine stops to ensure the London club went five matches on the road without defeat in the English top flight.
But the video assistant referee stepped in, advising the match official to check the score on the pitchside monitor and the official ruled that Jack Grealish and the attacker were in offside positions and had impeded with the Tottenham goalkeeper.
This victory elevates Thomas Frank's side up to third in the Premier League, five points off local foes and leaders the Gunners.
Everton remain 14th and are half a dozen points ahead of the drop zone.
After a uninspiring weekday display in the European competition against Monaco, where they managed a mere attempts on goal, Frank chose Randal Kolo Muani in attack instead of former Toffees player Richarlison.
The new arrival was failed to influence the game before being replaced for the substitute after an hour on the field, but it emerged he proved unnecessary in the end.
Defender the Dutchman transformed into an attacking force to be feared.
Spurs' first goal came from a well-worked set-piece play, with the midfielder heading the ball back across the six-yard box for an free Van de Ven to head home.
And the captain - filling in as captain in Cristian Romero's unavailability - added his next goal in first-half stoppage time as he outjumped the England keeper to nod in.
Van de Ven was just as impressive in defensive duties, partnering effectively with his defensive colleague as the duo dealt superbly with the 34 crosses sent their way by Everton.
The club's new home had been a fortress, but it appears the novelty may have faded somewhat and fans headed to the exits after Sarr's final goal for Spurs.
The end in the team's unbeaten home run won't be a massive concern for the manager, but their attacking woes are.
Beto and Thierno Barry - the Toffees' two established strikers - had scored only a single goal between them before Sunday's match.
And they were unable to add to that poor record on a damp and dreary night on in Liverpool.
Beto's form was summed up when he opted to overhead kick a golden opportunity from near the goal, even with having room and opportunity to readjust for a simpler attempt that would have challenged Vicario.
Barry, too, was unable to influence the game after replacing the starter in the 65th minute.
It was not for a shortage of chance. Most of the home side's attacks came through Grealish and the forward, who relentlessly delivered threatening crosses into the Spurs box.
Everton: The team travel to the Stadium of Light in the top flight on early November at 8 PM.
Tottenham: The London club go to Newcastle's ground on Wednesday, 29 October for their next round League Cup tie against the Magpies.
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