The Dutch defender emerged as the initial backline player to score twice in a Premier League game for Spurs since the Belgian defender in March 2013.
Key points
The Spurs defender nods home two times in first half
Everton's Jake O'Brien has goal ruled after VAR review
Senegalese midfielder nets third in 89th minute
The defeat is the Merseyside club's initial at their new ground
Micky van de Ven scored twice as Tottenham extended their unbeaten run in away games in the top division and handed Everton their initial loss at Hill Dickinson Stadium.
Everton were unbeaten in their last five matches at their new ground at Bramley-Moore Dock, having left Goodison Park behind after 133 years at the end of the previous campaign.
But Tottenham's leader the Dutchman struck on two occasions from set-pieces in the first half to put their impressive record at risk, and they were failed to turn it around before the midfielder - assisted by former Toffees attacker the Brazilian - nodded in a third to put the game to bed.
The Everton defender thought he had levelled the scores five minutes after Van de Ven's first goal, glancing 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 fine saves to ensure the London club went five matches on the road unbeaten in the Premier League.
But the VAR stepped in, advising the match official to review the score on the screen and the referee decided that the winger and Iliman Ndiaye were in offside positions and had interfered with the Tottenham goalkeeper.
The win moves the manager's side into third place in the Premier League, five points off north London rivals and table-toppers the Gunners.
Everton remain 14th and are half a dozen points ahead of the drop zone.
Following a drab weekday performance in the Champions League against Monaco, where they managed a only two shots on target, the manager chose the French striker up front instead of ex-Everton forward the Brazilian.
The new arrival was unable to influence the game before being substituted for the substitute after 60 minutes on the field, but it emerged he wasn't needed in the end.
Defender Van de Ven converted into an offensive threat to be feared.
Tottenham's first goal came from a well-worked corner routine, with Rodrigo Bentancur directing the ball back across the six-yard box for an free Van de Ven to score.
And the captain - filling in as captain in Cristian Romero's absence - added his second in first-half stoppage time as he outjumped Jordan Pickford to head home.
Van de Ven was just as impressive in defensive duties, partnering effectively with Kevin Danso as the pair handled superbly with the numerous deliveries thrown their way by Everton.
Everton's recent stadium had been a fortress, but it seems the novelty may have worn off somewhat and fans flocked to the exits after the midfielder's final goal for Spurs.
The break in the team's unbeaten home run won't be a major concern for David Moyes, but their striker situation will be.
Beto and the other striker - the Everton's two established strikers - had netted just a single goal between them before Sunday's outing.
And they were unable to add to that miserable tally on a wet and gloomy night on Merseyside.
The striker's form was epitomized when he opted to overhead kick a clear chance from near the goal, despite having space and opportunity to readjust for a simpler shot that would have challenged the keeper.
The substitute, too, was unable to make an impact after replacing Beto in the second half.
It wasn't for a shortage of opportunity. Most of Everton's offensive moves came through the winger and the forward, who tirelessly delivered threatening crosses into the Spurs box.
Everton: The team head to the Stadium of Light in the Premier League on Monday, 3 November at 8 PM.
Tottenham: Spurs travel to Newcastle's ground on late October for their next round Carabao Cup match against Newcastle.
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