Micky van de Ven Double Ends The Toffees' Run at New Stadium
The Dutch defender became the first defender to net twice in a English top-flight match for Spurs since Jan Vertonghen in March 2013.
Match summary
Micky Van de Ven nods into the net two times in opening period
Everton's Jake O'Brien has equalizer disallowed after VAR review
Pape Matar Sarr scores final goal in dying moments
The defeat is the Merseyside club's first at Hill Dickinson Stadium
The Tottenham defender found the net twice as Spurs 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 five previous fixtures at their recently opened stadium at the dockside location, having left Goodison Park behind after more than a century at the end of last season.
But Tottenham's leader the Dutchman pounced on two occasions from set-pieces in the opening 45 minutes to place their strong form at jeopardy, and they were unable to mount a comeback before the midfielder - set up by former Toffees attacker the Brazilian - headed home a third to seal the victory.
The Everton defender believed he had equalized the scores a short while after the defender's first goal, directing a powerful header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, in the meantime, failed to convert a number of chances, while Vicario made a series of fine stops to guarantee the London club went five matches on the road unbeaten in the English top flight.
But the VAR stepped in, instructing Craig Pawson to check the goal on the pitchside monitor 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 Premier League, a handful of points off local foes and leaders the Gunners.
Everton stay 14th and sit six points clear of the drop zone.
Tottenham analysis: The defender excels in role at each end of the field
After a drab weekday display in the Champions League against Monaco, where they managed a mere two shots on goal, Frank chose the French striker up front instead of former Toffees player the Brazilian.
The summer signing was unable to make much of an impact before being substituted for Richarlison after an hour on the pitch, but it turns out he proved unnecessary in the end.
Centre-back the Dutchman transformed into an offensive threat to be feared.
Tottenham's first goal came from a cleverly executed corner routine, with Rodrigo Bentancur directing the ball back across the face of goal for an free the defender to score.
And the captain - stepping up as skipper in Cristian Romero's absence - added his next goal in first-half stoppage time as he rose above Jordan Pickford to nod in.
The Dutchman was equally outstanding in defence, partnering effectively with his defensive colleague as the duo dealt excellently with the 34 crosses sent their way by Everton.
Everton analysis: Everton lacking striker's instinct
The club's new home had been a fortress, but it seems the freshness may have worn off somewhat and supporters headed to the exits after Sarr's third for Tottenham.
The end in Everton's unbeaten home run won't be a massive concern for David Moyes, but their striker situation are.
The forward and Thierno Barry - the Everton's pair of recognised centre-forwards - had scored only a single goal between them before Sunday's outing.
And they were unable to add to that miserable record on a damp and dreary night on in Liverpool.
The striker's form was epitomized when he chose to bicycle-kick a golden opportunity from near the goal, even with having space and opportunity to readjust for a more conventional shot that would have tested the keeper.
The substitute, as well, failed to make an impact after replacing Beto in the second half.
It was not for a lack of chance. The majority of Everton's offensive moves came through Grealish and the forward, who tirelessly delivered dangerous balls into the Tottenham penalty area.
Upcoming fixtures for both teams?
Everton: Moyes' men head to the Stadium of Light in the Premier League on early November at 8 PM.
Spurs: The London club go to Newcastle's ground on late October for their fourth-round Carabao Cup tie against the Magpies.