Micky van de Ven emerged as the first defender to score two goals in a Premier League game for Spurs since the Belgian defender in spring 2013.
At a glance
The Spurs defender heads into the net twice in first half
The home side's defender has equalizer disallowed after VAR review
Senegalese midfielder scores third in dying moments
This loss is Everton's first at Hill Dickinson Stadium
Micky van de Ven found the net twice as Tottenham prolonged their winning streak on the road in the Premier League and delivered Everton their initial loss at their new home.
The Toffees were unbeaten in their five previous fixtures at their new ground at the dockside location, having departed their historic home behind after 133 years at the conclusion of last season.
But Tottenham's leader the Dutchman struck twice from corners in the opening 45 minutes to put their impressive record at jeopardy, and they were failed to turn it around before Pape Matar Sarr - set up by former Toffees attacker Richarlison - nodded in a third to put the game to bed.
Jake O'Brien believed he had levelled the scores a short while after the defender's opener, glancing a bullet header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, in the meantime, failed to convert a handful of chances, while the Italian goalkeeper made a succession of excellent stops to guarantee Tottenham went five matches on the road unbeaten in the Premier League.
But the VAR intervened, instructing the match official to check the goal on the screen and the official ruled that Jack Grealish and the attacker were in offside positions and had interfered with the Spurs keeper.
The win moves Thomas Frank's team into third place in the Premier League, five points off north London rivals and leaders the Gunners.
The Merseyside club stay in 14th position and are half a dozen points ahead of the relegation zone.
After a drab weekday performance in the European competition against Monaco, where they managed a only attempts on goal, the manager opted for Randal Kolo Muani in attack instead of ex-Everton forward the Brazilian.
The summer signing was unable to make much of an impact before being replaced for the substitute after an hour on the pitch, but it emerged he wasn't needed in the final outcome.
Defender the Dutchman converted into an attacking force to be feared.
Tottenham's first goal came from a well-worked corner routine, with the midfielder heading the ball back across the face of goal for an free Van de Ven to head home.
And Ven de Ven - filling in as skipper in the Argentine's absence - added his second in first-half stoppage time as he rose above Jordan Pickford to nod in.
Van de Ven was just as outstanding in defence, partnering well with Kevin Danso as the duo dealt excellently with the 34 crosses sent their way by Everton.
The club's new home had been a fortress, but it seems the freshness may have faded somewhat and fans headed to the exits after the midfielder's third for Tottenham.
The end in the team's unbeaten home run won't be a major worry for David Moyes, but their attacking woes will be.
Beto and Thierno Barry - the Everton's pair of recognised centre-forwards - had scored only a single goal combined before Sunday's outing.
And they were unable to add to that miserable tally on a wet and gloomy night on in Liverpool.
The striker's form was epitomized when he opted to bicycle-kick a clear chance from near the goal, despite having space and opportunity to reposition for a more conventional shot that would have tested the keeper.
The substitute, too, was unable to make an impact after replacing Beto in the 65th minute.
It wasn't for a shortage of opportunity. Most of Everton's offensive moves came through Grealish and the forward, who relentlessly whipped threatening crosses into the Spurs penalty area.
The Toffees: The team head to Sunderland in the Premier League on Monday, 3 November at 8 PM.
Tottenham: Spurs travel to St James' Park on late October for their fourth-round Carabao Cup match against Newcastle.
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Michelle Beard
Michelle Beard
Michelle Beard
Michelle Beard
Michelle Beard
Michelle Beard