Micky van de Ven Double Halts The Toffees' Run at Brand New Home Ground
The Dutch defender emerged as the initial defender to score twice in a English top-flight 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 Jake O'Brien has goal ruled after video check
Pape Matar Sarr nets third in dying moments
This loss is the Merseyside club's initial at Hill Dickinson Stadium
Micky van de Ven found the net twice as Spurs extended their unbeaten run on the road in the top division and delivered the Toffees their initial loss at Hill Dickinson Stadium.
Everton were undefeated in their five previous fixtures at their recently opened stadium at Bramley-Moore Dock, having departed Goodison Park behind after more than a century at the end of the previous campaign.
But Spurs captain the Dutchman pounced on two occasions from set-pieces in the first half to place their impressive record at jeopardy, and they were unable to turn it around before the midfielder - assisted by ex-Everton forward the Brazilian - headed home a final goal to seal the victory.
Jake O'Brien thought he had levelled the tally five minutes after Van de Ven's opener, glancing a powerful header past Guglielmo Vicario from an set-piece.
Beto, in the meantime, failed to convert a number of opportunities, while Vicario made a succession of fine stops to guarantee Tottenham went five away games without defeat in the English top flight.
But the video assistant referee intervened, advising Craig Pawson to check the score on the screen and the referee decided that the winger and the attacker were in offside positions and had interfered with the Spurs keeper.
This victory moves the manager's team up to third in the Premier League, five points off north London rivals and table-toppers the Gunners.
Everton remain in 14th position and sit six points ahead of the drop zone.
Tottenham analysis: Van de Ven fulfils role at both ends of the field
After a uninspiring weekday performance in the European competition against the French side, where they mustered a mere two shots on target, the manager opted for Randal Kolo Muani in attack instead of former Toffees player the Brazilian.
The summer signing was unable to make much of an impact before being replaced for Richarlison after 60 minutes on the field, but it turns out he wasn't needed in the final outcome.
Defender Van de Ven converted into an offensive threat to be feared.
Spurs' opening strike came from a well-worked corner routine, with Rodrigo Bentancur heading the ball toward the face of goal for an free Van de Ven to head home.
And the captain - stepping up as captain in the Argentine's unavailability - notched his second in added time as he outjumped Jordan Pickford to head home.
The Dutchman was just as outstanding in defence, combining effectively with Kevin Danso as the pair handled superbly with the 34 crosses sent their way by the opposition.
Toffees breakdown: Toffees missing finishing touch
The club's recent stadium had been a happy hunting ground, but it seems the freshness may have faded slightly and supporters flocked to the gates after the midfielder's final goal for Tottenham.
The end in Everton's unbeaten home run will not be a major worry for the manager, but their attacking woes will be.
The forward and Thierno Barry - the Toffees' pair of established strikers - had scored just a single goal combined before Sunday's outing.
And they were unable to add to that poor record on a wet and gloomy night on Merseyside.
Beto's performance was summed up when he opted to bicycle-kick a clear chance from close range, despite having space and time to reposition for a more conventional shot that would have tested Vicario.
The substitute, too, was unable to influence the game after coming on for the starter in the 65th minute.
It was not for a shortage of chance. The majority of the home side's attacks came through Grealish and the forward, who tirelessly whipped dangerous balls into the Tottenham box.
What next for both teams?
The Toffees: Moyes' men travel to the Stadium of Light in the Premier League on early November at 20:00 GMT.
Tottenham: The London club travel to St James' Park on Wednesday, 29 October for their fourth-round Carabao Cup match against the Magpies.