Micky van de Ven emerged as the initial backline player to score two goals in a English top-flight game for Spurs since Jan Vertonghen in March 2013.
Match summary
The Spurs defender nods home two times in opening period
The home side's defender has equalizer ruled after VAR review
Pape Matar Sarr scores third in 89th minute
The defeat is the Merseyside club's first at their new ground
The Tottenham defender found the net on two occasions as Spurs extended their unbeaten run in away games in the top division and handed Everton their first defeat at Hill Dickinson Stadium.
The Toffees were unbeaten in their five previous fixtures at their new ground at the dockside location, having left their historic home behind after more than a century at the end of the previous campaign.
But Spurs captain the Dutchman struck on two occasions from set-pieces in the opening 45 minutes to put their impressive record 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 seal the victory.
Jake O'Brien believed he had equalized the tally five minutes after the defender's first goal, directing a powerful header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, in the meantime, missed a number of opportunities, while Vicario made a series of excellent saves to ensure the London club went five matches on the road without defeat in the English top flight.
But the VAR stepped in, instructing Craig Pawson to review the score on the screen and the referee ruled that the winger and the attacker were in an illegal position and had interfered with the Tottenham goalkeeper.
This victory elevates Thomas Frank's team up to third in the division, five points off north London rivals and table-toppers Arsenal.
The Merseyside club remain 14th and sit six points clear of the drop zone.
After a uninspiring weekday performance in the Champions League against Monaco, where they managed a mere attempts on goal, Frank opted for the French striker up front instead of ex-Everton forward the Brazilian.
The new arrival was unable to make much of an impact before being replaced for Richarlison after 60 minutes on the pitch, but it turns out he proved unnecessary in the end.
Defender Van de Ven transformed into an offensive threat to be feared.
Tottenham's first goal came from a cleverly executed set-piece play, with Rodrigo Bentancur heading the ball toward the face of goal for an unmarked Van de Ven to head home.
And Ven de Ven - filling in as captain in Cristian Romero's absence - added his next goal in added time as he rose above Jordan Pickford to nod in.
The Dutchman was equally outstanding in defence, combining effectively with his defensive colleague as the pair handled excellently with the numerous deliveries sent their way by Everton.
The club's new home had been a happy hunting ground, but it seems the novelty may have faded slightly and supporters flocked to the exits after the midfielder's final goal for Tottenham.
The break in Everton's unbeaten home run will not be a massive concern for the manager, but their attacking woes are.
Beto and Thierno Barry - the Toffees' two recognised strikers - had scored just a single goal between them before the weekend's match.
And they were failed to contribute to that miserable tally on a damp and dreary night on in Liverpool.
The striker's performance was summed up when he opted to bicycle-kick a golden opportunity from close range, even with having space and opportunity to readjust for a more conventional attempt that would have tested Vicario.
Barry, too, failed to influence the game after replacing Beto in the second half.
It was not for a shortage of chance. The majority of Everton's attacks came through the winger and the forward, who relentlessly whipped threatening balls into the Spurs penalty area.
The Toffees: The team travel to Sunderland in the top flight on Monday, 3 November at 8 PM.
Spurs: The London club go to St James' Park on late October for their next round League Cup tie against the Magpies.
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