Micky van de Ven Brace Ends Everton's Run at New Home Ground
The Dutch defender became the initial backline player to net twice in a Premier League match for Spurs since the Belgian defender in spring 2013.
Match summary
The Spurs defender heads home two times in opening period
The home side's Jake O'Brien has equalizer ruled after VAR review
Pape Matar Sarr scores final goal in dying moments
This loss is Everton's first at Hill Dickinson Stadium
The Tottenham defender scored on two occasions as Tottenham extended their unbeaten run in away games in the top division and handed Everton their initial loss at Hill Dickinson Stadium.
The Toffees were unbeaten in their last five matches at their new ground at Bramley-Moore Dock, having left their historic home behind after 133 years at the end of last season.
But Spurs captain the Dutchman struck on two occasions from corners in the first half to put their impressive record at jeopardy, and they were unable to turn it around before the midfielder - set up by former Toffees attacker the Brazilian - headed home a third to seal the victory.
The Everton defender thought he had levelled the scores a short while after the defender's opener, glancing a powerful header past the Spurs keeper from an Everton corner.
The Portuguese striker, in the meantime, missed a handful of opportunities, while the Italian goalkeeper made a series of fine saves 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 pitchside monitor and the referee decided that Jack Grealish and the attacker were in an illegal position and had impeded with the Tottenham goalkeeper.
The win moves the manager's team up to third in the Premier League, a handful of points off local foes and leaders the Gunners.
The Merseyside club remain in 14th position and sit six points clear of the drop zone.
Spurs breakdown: Van de Ven excels in role at each end of pitch
Following a drab midweek display in the European competition against the French side, where they mustered a only two shots on target, Frank opted for the French striker in attack instead of former Toffees player Richarlison.
The summer signing was failed to make much of an impact before being substituted for Richarlison after 60 minutes on the pitch, but it emerged he proved unnecessary in the final outcome.
Defender the Dutchman converted into an attacking force to be feared.
Tottenham's first goal came from a well-worked set-piece play, with Rodrigo Bentancur directing the ball back across the six-yard box for an unmarked Van de Ven to head home.
And the captain - filling in as skipper in the Argentine's unavailability - added his next goal in added time as he rose above the England keeper to head home.
The Dutchman was just as outstanding in defence, partnering effectively with Kevin Danso as the duo dealt excellently with the numerous deliveries thrown their way by the opposition.
Everton analysis: Toffees missing finishing touch
Everton's recent stadium had been a happy hunting ground, but it seems the novelty may have faded slightly and fans headed to the exits after Sarr's third for Spurs.
The end in Everton's winning streak at home won't be a major concern for David Moyes, but their striker situation will be.
Beto and Thierno Barry - the Toffees' two established strikers - had netted only one league goal between them before the weekend's outing.
And they were failed to add to that poor tally on a wet and gloomy night on Merseyside.
Beto's performance was summed up when he opted to bicycle-kick a clear chance from near the goal, even with having space and time to readjust for a simpler attempt that would have challenged the keeper.
The substitute, as well, failed to influence the game after coming on for the starter in the second half.
It was not for a lack of chance. Most of Everton's attacks came through the winger and the forward, who relentlessly whipped dangerous balls into the Spurs box.
What next for these two sides?
Everton: Moyes' men travel to the Stadium of Light in the top flight on early November at 20:00 GMT.
Spurs: The London club go to St James' Park on Wednesday, 29 October for their fourth-round Carabao Cup match against the Magpies.