Micky van de Ven became the first backline player to score twice in a Premier League game for Spurs since the Belgian defender in March 2013.
At a glance
Micky Van de Ven nods home twice in opening period
The home side's defender has equalizer disallowed after VAR review
Pape Matar Sarr scores final goal in 89th minute
The defeat is Everton's initial at their new ground
Micky van de Ven found the net twice as Spurs prolonged their winning streak on the road in the top division and handed the Toffees their first defeat at Hill Dickinson Stadium.
Everton were unbeaten in their last five matches at their recently opened stadium at Bramley-Moore Dock, having departed Goodison Park behind after 133 years at the conclusion of last season.
But Tottenham's leader Van de Ven struck on two occasions from corners in the first half to place their strong form at risk, and they were unable to mount a comeback before Pape Matar Sarr - set up by ex-Everton forward Richarlison - headed home a final goal to seal the victory.
Jake O'Brien believed he had levelled the tally a short while after Van de Ven's opener, directing a bullet header past Guglielmo Vicario from an set-piece.
Beto, in the meantime, missed a number of opportunities, while the Italian goalkeeper made a series of fine stops to guarantee Tottenham went five away games without defeat in the English top flight.
But the VAR intervened, advising the match official to review the score on the screen and the official decided that the winger and Iliman Ndiaye were in an illegal position and had interfered with the Spurs keeper.
This victory moves Thomas Frank's side up to third in the division, a handful of points off north London rivals and leaders Arsenal.
Everton stay 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 only attempts on goal, Frank opted for the French striker in attack instead of ex-Everton forward Richarlison.
The summer signing was failed to make much of an impact before being substituted 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 offensive threat to be feared.
Spurs' opening strike came from a well-worked set-piece play, with the midfielder heading the ball toward the six-yard box for an free the defender to head home.
And the captain - stepping up as captain in the Argentine's unavailability - notched his next goal in added time as he rose above Jordan Pickford to nod in.
The Dutchman was equally impressive in defensive duties, partnering well with Kevin Danso as the pair handled excellently with the 34 crosses sent their way by the opposition.
The club's recent stadium had been a happy hunting ground, but it seems the novelty may have faded slightly and fans flocked to the exits after Sarr's third for Tottenham.
The break in the team's winning streak at home won't be a major concern for the manager, but their striker situation will be.
Beto and the other striker - the Toffees' two recognised strikers - had scored just a single goal combined before the weekend's match.
And they were failed to contribute to that miserable record on a wet and gloomy night on Merseyside.
The striker's performance was summed up when he chose to overhead kick a clear chance from near the goal, despite having space and opportunity to reposition for a simpler shot that would have challenged the keeper.
The substitute, as well, failed to make an impact after replacing the starter in the 65th minute.
It was not for a lack of chance. Most of Everton's offensive moves came through the winger and the forward, who tirelessly whipped dangerous crosses into the Spurs box.
The Toffees: The team travel to Sunderland in the Premier League on early November at 20:00 GMT.
Tottenham: Spurs go to Newcastle's ground on Wednesday, 29 October for their next round League Cup tie against Newcastle.
Lena Hoffmann is a seasoned journalist with a passion for uncovering stories that matter, specializing in German current affairs and digital media trends.
