Micky van de Ven became the initial defender to score two goals in a English top-flight game for Tottenham since Jan Vertonghen in spring 2013.
Key points
Micky Van de Ven nods into the net two times in first half
Everton's Jake O'Brien has goal disallowed after VAR review
Senegalese midfielder nets third in 89th minute
This loss is the Merseyside club's initial at Hill Dickinson Stadium
The Tottenham defender found the net twice as Spurs prolonged their winning streak in away games in the Premier League and delivered the Toffees their initial loss at their new home.
Everton were undefeated in their last five matches at their recently opened stadium at Bramley-Moore Dock, having departed their historic home behind after 133 years at the conclusion of the previous campaign.
But Tottenham's leader Van de Ven pounced on two occasions from corners in the first half to place their strong form at jeopardy, and they were failed to mount a comeback before the midfielder - set up by ex-Everton forward Richarlison - headed home a final goal to seal the victory.
The Everton defender thought he had levelled the tally a short while after the defender's opener, directing a bullet header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, in the meantime, failed to convert a number of opportunities, while the Italian goalkeeper made a succession of excellent saves to ensure the London club went five away games without defeat in the Premier League.
But the VAR intervened, advising Craig Pawson to check the goal on the screen and the referee ruled that Jack Grealish and the attacker were in offside positions and had impeded with the Tottenham goalkeeper.
This victory elevates Thomas Frank's team into third place in the division, five points off local foes and leaders the Gunners.
The Merseyside club remain in 14th position and are half a dozen points ahead of the relegation zone.
Following a drab weekday display in the European competition against the French side, where they managed a mere attempts on goal, Frank chose the French striker in attack instead of former Toffees player Richarlison.
The summer signing was unable to make much of an impact before being substituted for the substitute after an hour on the field, but it turns out he proved unnecessary in the final outcome.
Centre-back the Dutchman transformed into an offensive threat to be feared.
Tottenham's first goal came from a cleverly executed set-piece play, with Rodrigo Bentancur directing the ball back across the six-yard box for an free the defender to head home.
And Ven de Ven - filling in as skipper in the Argentine's unavailability - notched his next goal in added time as he outjumped Jordan Pickford to nod in.
Van de Ven was just as outstanding in defensive duties, partnering well with his defensive colleague as the duo handled excellently with the numerous deliveries thrown their way by Everton.
The club's new home had been a happy hunting ground, but it seems the novelty may have worn off slightly and supporters headed to the gates after the midfielder's final goal for Spurs.
The end in the team's unbeaten home run will not be a major concern for the manager, but their striker situation will be.
Beto and the other striker - the Toffees' pair of recognised strikers - had netted just one league goal combined before the weekend's match.
And they were unable to contribute to that poor record on a wet and gloomy evening on Merseyside.
The striker's performance was summed up when he opted to overhead kick a clear chance from close range, even with having room and opportunity to readjust for a simpler shot that would have tested Vicario.
Barry, too, was unable to make an impact after replacing Beto in the second half.
It was not for a shortage of opportunity. The majority of the home side's offensive moves came through Grealish and the forward, who tirelessly whipped dangerous balls into the Tottenham box.
Everton: The team head to Sunderland in the top flight on Monday, 3 November at 8 PM.
Tottenham: The London club travel to Newcastle's ground on Wednesday, 29 October for their fourth-round Carabao Cup tie against the Magpies.
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