Micky van de Ven Double Ends Everton's Run at Brand New Stadium
The Dutch defender emerged as the first defender to net twice in a Premier League game for Tottenham since the Belgian defender in March 2013.
At a glance
Micky Van de Ven heads home twice in opening period
The home side's Jake O'Brien has goal disallowed after video check
Senegalese midfielder nets final goal in 89th minute
The defeat is Everton's initial at Hill Dickinson Stadium
The Tottenham defender found the net twice as Spurs prolonged their winning streak in away games in the Premier League and delivered the Toffees their first defeat at Hill Dickinson Stadium.
The Toffees were unbeaten in their five previous fixtures at their recently opened stadium at the dockside location, having departed their historic home behind after 133 years at the conclusion of the previous campaign.
But Tottenham's leader the Dutchman struck on two occasions from corners in the opening 45 minutes to put their impressive record at risk, and they were unable to turn it around before the midfielder - assisted by former Toffees attacker the Brazilian - nodded in a final goal to put the game to bed.
The Everton defender thought he had levelled the tally a short while after Van de Ven's opener, directing a powerful header past Guglielmo Vicario from an set-piece.
Beto, meanwhile, missed a number of opportunities, while the Italian goalkeeper made a series of fine stops to ensure the London club went five away games unbeaten in the English top flight.
But the video assistant referee intervened, instructing the match official to check the score on the screen and the official decided that the winger and the attacker were in an illegal position and had impeded with the Spurs keeper.
This victory elevates Thomas Frank's side up to third in the division, a handful of points off north London rivals and leaders the Gunners.
The Merseyside club stay in 14th position and are six points ahead of the relegation zone.
Spurs breakdown: The defender excels in duties at both ends of the field
After a uninspiring midweek performance in the European competition against the French side, where they managed a mere attempts on goal, Frank chose the French striker up front instead of former Toffees player the Brazilian.
The new arrival 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 end.
Defender the Dutchman converted into an attacking force to be reckoned with.
Tottenham's first goal came from a well-worked corner routine, with the midfielder heading the ball back across the six-yard box for an free Van de Ven to score.
And Ven de Ven - filling in as skipper in Cristian Romero's absence - notched his next goal in added time as he rose above Jordan Pickford to head home.
Van de Ven was equally impressive in defence, combining well with Kevin Danso as the duo dealt excellently with the 34 crosses sent their way by the opposition.
Toffees breakdown: Everton missing finishing touch
The club's recent stadium had been a fortress, but it seems the novelty may have faded slightly and fans headed to the exits after the midfielder's third for Spurs.
The break in Everton's unbeaten home run won't be a major worry for the manager, but their striker situation will be.
The forward and the other striker - the Toffees' pair of recognised strikers - had netted only a single goal combined before the weekend's outing.
And they were failed to contribute to that miserable tally on a damp and dreary evening on Merseyside.
Beto's form was summed up when he opted to bicycle-kick a clear chance from near the goal, despite having room and time to reposition for a simpler shot that would have challenged the keeper.
Barry, as well, was unable to influence the game after coming on for the starter in the 65th minute.
It was not for a shortage of opportunity. The majority of Everton's attacks came through Grealish and the forward, who tirelessly delivered threatening crosses into the Tottenham penalty area.
Upcoming fixtures for these two sides?
Everton: Moyes' men travel to the Stadium of Light in the Premier League on early November at 8 PM.
Tottenham: The London club go to St James' Park on Wednesday, 29 October for their fourth-round Carabao Cup tie against the Magpies.