The Dutch defender emerged as the first defender to score twice in a Premier League game for Tottenham since the Belgian defender in spring 2013.
Key points
The Spurs defender heads home twice in first half
Everton's defender has equalizer ruled after video check
Pape Matar Sarr scores third in dying moments
The defeat is Everton's initial at Hill Dickinson Stadium
Micky van de Ven scored on two occasions as Tottenham prolonged their winning streak in away games in the Premier League and delivered Everton their initial loss at Hill Dickinson Stadium.
The Toffees were undefeated in their last five matches at their recently opened stadium at the dockside location, having left Goodison Park behind after 133 years at the end of last season.
But Tottenham's leader Van de Ven struck on two occasions from corners in the opening 45 minutes to put their strong form at risk, and they were failed to turn it around before Pape Matar Sarr - assisted by former Toffees attacker the Brazilian - nodded in a third to put the game to bed.
Jake O'Brien thought he had equalized the tally a short while after Van de Ven's first goal, directing a powerful header past the Spurs keeper from an set-piece.
Beto, in the meantime, failed to convert a number of chances, while Vicario made a succession of excellent saves to guarantee Tottenham went five away games without defeat in the English top flight.
But the video assistant referee intervened, advising the match official to check the goal on the screen and the referee decided that the winger and the attacker were in an illegal position and had interfered with the Tottenham goalkeeper.
This victory moves Thomas Frank's team into third place in the division, a handful of points off north London rivals and table-toppers the Gunners.
The Merseyside club stay 14th and sit six points ahead of the drop zone.
After a drab midweek performance in the European competition against the French side, where they mustered a only two shots on target, Frank chose the French striker up front instead of ex-Everton forward Richarlison.
The summer signing was unable 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 Van de Ven converted into an offensive threat to be reckoned with.
Tottenham's first goal came from a well-worked corner routine, with the midfielder directing the ball back across the face of goal for an free the defender to head home.
And the captain - stepping up as skipper in the Argentine's unavailability - notched his second in first-half stoppage time as he rose above the England keeper to head home.
The Dutchman was just as impressive in defensive duties, combining effectively with his defensive colleague as the duo handled excellently with the numerous deliveries sent their way by Everton.
Everton's recent stadium had been a fortress, but it seems the freshness may have worn off somewhat and fans headed to the exits after the midfielder's third for Tottenham.
The break in Everton's winning streak at home will not be a massive worry for David Moyes, but their attacking woes will be.
The forward and Thierno Barry - the Toffees' pair of recognised strikers - had scored only one league goal between them before Sunday's match.
And they were unable to add to that poor record on a wet and gloomy evening on Merseyside.
Beto's performance was epitomized when he chose to overhead kick a clear chance from near the goal, even with having room and time to readjust for a more conventional shot that would have challenged Vicario.
The substitute, as well, was unable to make an impact after replacing the starter in the 65th minute.
It was not for a shortage of opportunity. The majority of the home side's attacks came through the winger and the forward, who relentlessly delivered dangerous balls into the Spurs box.
The Toffees: Moyes' men head to the Stadium of Light in the top flight on Monday, 3 November at 8 PM.
Spurs: The London club travel to Newcastle's ground on Wednesday, 29 October for their next round Carabao Cup match against the Magpies.
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