The Dutch defender became the initial defender to net twice in a Premier League match for Spurs since Jan Vertonghen in spring 2013.
At a glance
Micky Van de Ven heads home twice in opening period
The home side's Jake O'Brien has equalizer ruled after VAR review
Pape Matar Sarr scores third in 89th minute
The defeat is the Merseyside club's initial at Hill Dickinson Stadium
Micky van de Ven found the net twice as Tottenham prolonged their unbeaten run on the road in the Premier League and delivered the Toffees their first defeat at their new home.
Everton were unbeaten in their five previous fixtures at their recently opened stadium at Bramley-Moore Dock, having left their historic home behind after more than a century at the conclusion of last season.
But Tottenham's leader the Dutchman pounced on two occasions from set-pieces in the opening 45 minutes to place their strong form at risk, and they were failed to turn it around before Pape Matar Sarr - set up by ex-Everton forward the Brazilian - nodded in a final goal to put the game to bed.
Jake O'Brien thought he had levelled the scores five minutes after Van de Ven's first goal, directing a powerful header past Guglielmo Vicario from an Everton corner.
Beto, in the meantime, missed a number of chances, while Vicario made a series of fine stops to guarantee Tottenham went five away games unbeaten in the Premier League.
But the VAR stepped in, advising the match official to review the score on the screen and the official decided that the winger and Iliman Ndiaye were in offside positions and had interfered with the Spurs keeper.
The win moves the manager's side into third place in the division, five points off local foes and leaders Arsenal.
Everton stay 14th and are six points clear of the relegation zone.
After a uninspiring midweek display in the European competition against Monaco, where they mustered a only attempts on target, the manager chose Randal Kolo Muani in attack instead of former Toffees player Richarlison.
The new arrival was unable to influence the game before being substituted for the substitute after an hour on the field, but it turns out he wasn't needed in the final outcome.
Defender the Dutchman converted into an attacking force to be reckoned with.
Tottenham's first goal came from a well-worked set-piece play, with Rodrigo Bentancur heading the ball back across the face of goal for an free the defender to head home.
And the captain - filling in as skipper in Cristian Romero's unavailability - notched his second in first-half stoppage time as he rose above Jordan Pickford to head home.
The Dutchman was just as impressive in defence, combining effectively with his defensive colleague as the duo handled superbly with the numerous deliveries sent their way by Everton.
The club's recent stadium had been a happy hunting ground, but it seems the novelty may have worn off slightly and supporters flocked to the gates after the midfielder's third for Tottenham.
The break in the team's unbeaten home run will not be a major worry for David Moyes, but their attacking woes are.
The forward and the other striker - the Everton's two established centre-forwards - had netted just one league goal combined before the weekend's match.
And they were failed to contribute to that miserable tally on a damp and dreary evening on in Liverpool.
Beto's form was summed up when he opted to bicycle-kick a golden opportunity from near the goal, even with having space and time to readjust for a simpler attempt that would have tested Vicario.
Barry, too, was unable to make an impact after replacing Beto in the 65th minute.
It wasn't for a lack of chance. Most of the home side's offensive moves came through the winger and the forward, who tirelessly delivered threatening crosses into the Spurs box.
The Toffees: Moyes' men head to Sunderland in the top flight on early November at 8 PM.
Tottenham: Spurs travel to Newcastle's ground on Wednesday, 29 October for their fourth-round League Cup tie against Newcastle.
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Monica Leonard
Monica Leonard
Monica Leonard
Monica Leonard