Micky van de Ven Brace Halts Everton's Run at Brand New Stadium
The Dutch defender emerged as the first backline player to net two goals in a English top-flight game for Spurs since Jan Vertonghen in March 2013.
Match summary
Micky Van de Ven heads into the net twice in first half
The home side's defender has goal disallowed after video check
Senegalese midfielder scores final goal in 89th minute
The defeat is Everton's initial at Hill Dickinson Stadium
The Tottenham defender scored on two occasions as Tottenham prolonged their unbeaten run on the road in the Premier League and delivered the Toffees their initial loss at their new home.
Everton were unbeaten in their five previous fixtures at their new ground at the dockside location, having left Goodison Park behind after more than a century at the end of the previous campaign.
But Tottenham's leader Van de Ven struck on two occasions from corners in the opening 45 minutes to put their impressive record at jeopardy, and they were unable to turn it around before the midfielder - set up by former Toffees attacker Richarlison - nodded in a final goal to seal the victory.
The Everton defender thought he had equalized the tally a short while after Van de Ven's first goal, glancing a bullet header past the Spurs keeper from an set-piece.
Beto, in the meantime, missed a handful of chances, while the Italian goalkeeper made a series of excellent stops to guarantee the London club went five matches on the road without defeat in the English top flight.
But the VAR intervened, advising the match official to review the score on the pitchside monitor and the official decided that the winger and the attacker were in an illegal position and had interfered with the Spurs keeper.
The win elevates Thomas Frank's side into third place in the division, a handful of points off north London rivals and leaders Arsenal.
Everton stay 14th and sit half a dozen points clear of the relegation zone.
Tottenham analysis: Van de Ven excels in duties at each end of pitch
Following a drab midweek performance in the European competition against Monaco, where they managed a only two shots on goal, the manager opted for the French striker in attack instead of ex-Everton forward the Brazilian.
The summer signing was failed to make much of an impact before being replaced for Richarlison after an hour on the pitch, but it emerged he wasn't needed in the end.
Defender the Dutchman converted into an offensive threat to be feared.
Spurs' first goal came from a cleverly executed set-piece play, with the midfielder heading the ball back across the face of goal for an unmarked Van de Ven to score.
And the captain - stepping up as captain in the Argentine's unavailability - notched his next goal in added time as he rose above the England keeper to head home.
The Dutchman was equally outstanding in defence, combining well with his defensive colleague as the pair dealt excellently with the 34 crosses sent their way by the opposition.
Everton analysis: Everton lacking striker's instinct
Everton's new home had been a fortress, but it appears the freshness may have faded somewhat and fans headed to the exits after the midfielder's final goal for Spurs.
The end in Everton's unbeaten home run won't be a major concern for the manager, but their attacking woes will be.
Beto and Thierno Barry - the Everton's two recognised strikers - had netted only one league goal between them before Sunday's match.
And they were unable to contribute to that poor tally on a wet and gloomy night on in Liverpool.
Beto's form was epitomized when he chose to overhead kick a clear chance from near the goal, despite having room and time to readjust for a more conventional attempt that would have challenged the keeper.
The substitute, too, was unable to make an impact after coming on for the starter in the 65th minute.
It was not for a shortage of chance. The majority of Everton's attacks came through Grealish and Ndiaye, who relentlessly whipped dangerous balls into the Tottenham box.
What next for these two sides?
The Toffees: Moyes' men travel to Sunderland in the top flight on early November at 20:00 GMT.
Spurs: The London club go to St James' Park on late October for their fourth-round League Cup tie against the Magpies.