Micky van de Ven became the initial backline player to net twice in a Premier League match for Tottenham since Jan Vertonghen in spring 2013.
Key points
The Spurs defender heads into the net twice in first half
Everton's Jake O'Brien has goal disallowed after VAR review
Senegalese midfielder nets third in 89th minute
The defeat is Everton's first at their new ground
The Tottenham defender scored twice as Spurs prolonged their winning streak in away games in the top division and handed Everton their initial loss at their new home.
Everton were undefeated in their five previous fixtures at their recently opened stadium at the dockside location, having departed their historic home behind after more than a century at the end of the previous campaign.
But Spurs captain Van de Ven struck twice from corners in the opening 45 minutes to put their strong form at jeopardy, and they were failed to mount a comeback before Pape Matar Sarr - assisted by ex-Everton forward Richarlison - nodded in a third to put the game to bed.
Jake O'Brien believed he had levelled the scores five minutes after the defender's opener, glancing a powerful header past the Spurs keeper from an set-piece.
The Portuguese striker, in the meantime, missed a handful of opportunities, while the Italian goalkeeper made a series of fine saves to guarantee Tottenham went five away games without defeat in the English top flight.
But the video assistant referee stepped in, advising the match official to review the score on the pitchside monitor and the referee decided that the winger and the attacker were in offside positions and had interfered with the Tottenham goalkeeper.
The win moves Thomas Frank's side into third place in the Premier League, a handful of points off local foes and table-toppers the Gunners.
The Merseyside club stay in 14th position and sit six points ahead of the drop zone.
After a uninspiring midweek performance in the European competition against Monaco, where they mustered a mere two shots on target, Frank chose Randal Kolo Muani in attack instead of ex-Everton forward Richarlison.
The new arrival was unable to make much of an impact before being substituted for the substitute after an hour on the field, but it emerged he proved unnecessary in the final outcome.
Defender Van de Ven transformed into an offensive threat to be reckoned with.
Spurs' opening strike came from a cleverly executed corner routine, with the midfielder directing the ball back across the six-yard box for an unmarked the defender to score.
And the captain - filling in as captain in the Argentine's unavailability - notched his next goal in first-half stoppage time as he outjumped Jordan Pickford to nod in.
The Dutchman was just as outstanding in defensive duties, combining well with his defensive colleague as the duo dealt excellently with the numerous deliveries thrown their way by the opposition.
The club's new home had been a happy hunting ground, but it seems the novelty may have faded somewhat and fans headed to the exits after the midfielder's final goal for Spurs.
The break in Everton's winning streak at home will not be a major concern for David Moyes, but their attacking woes are.
Beto and Thierno Barry - the Everton's two recognised centre-forwards - had netted just a single goal between them before the weekend's match.
And they were unable to contribute to that miserable tally on a damp and dreary evening on in Liverpool.
The striker's performance was epitomized when he opted to bicycle-kick a golden opportunity from close range, despite having room and time to readjust for a simpler shot that would have tested the keeper.
The substitute, as well, was unable to influence the game after replacing the starter in the second half.
It was not for a shortage of opportunity. The majority of Everton's offensive moves came through Grealish and Ndiaye, who relentlessly delivered dangerous balls into the Spurs penalty area.
The Toffees: The team head to Sunderland in the top flight on early November at 8 PM.
Spurs: The London club travel to St James' Park on late October for their fourth-round Carabao Cup tie against Newcastle.
A Scandinavian design enthusiast with over a decade of experience curating Nordic home decor and sharing minimalist living tips.