The Dutch defender became the initial backline player to score twice in a English top-flight match for Spurs since the Belgian defender in spring 2013.
Key points
The Spurs defender heads home twice in opening period
The home side's defender has goal ruled after video check
Senegalese midfielder nets third in 89th minute
The defeat is the Merseyside club's first at their new ground
The Tottenham defender scored on two occasions as Spurs extended their unbeaten run in away games in the Premier League and handed the Toffees their first defeat at Hill Dickinson Stadium.
The Toffees were unbeaten 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 conclusion of the previous campaign.
But Spurs captain the Dutchman struck on two occasions from corners in the opening 45 minutes to place their strong form at risk, and they were failed to turn it around before the midfielder - assisted by ex-Everton forward the Brazilian - headed home a final goal to put the game to bed.
Jake O'Brien believed he had levelled the tally a short while after the defender's first goal, glancing a bullet header past the Spurs keeper from an set-piece.
Beto, in the meantime, failed to convert a handful of opportunities, while Vicario made a series of excellent stops to guarantee the London club went five matches on the road without defeat in the Premier League.
But the VAR stepped in, advising the match official to check the score on the screen and the referee decided that Jack Grealish and the attacker were in an illegal position and had interfered with the Spurs keeper.
The win elevates Thomas Frank's team into third place in the Premier League, five points off north London rivals and leaders the Gunners.
Everton remain 14th and are half a dozen points ahead of the drop zone.
After a drab midweek display in the Champions League against Monaco, where they mustered a mere two shots on target, the manager chose the French striker up front instead of former Toffees player Richarlison.
The summer signing was failed to influence the game before being replaced for the substitute after 60 minutes on the pitch, but it turns out he wasn't needed in the final outcome.
Defender Van de Ven converted into an attacking force to be feared.
Spurs' opening strike came from a well-worked corner routine, with the midfielder heading the ball back across the face of goal for an free the defender to score.
And Ven de Ven - stepping up as skipper in Cristian Romero's unavailability - notched his next goal in added time as he rose above the England keeper to nod in.
The Dutchman was just as impressive in defensive duties, combining effectively with Kevin Danso as the pair dealt superbly with the numerous deliveries sent their way by the opposition.
Everton's new home had been a happy hunting ground, but it seems the freshness may have worn off somewhat and fans headed to the exits after the midfielder's final goal for Spurs.
The end in Everton's unbeaten home run will not be a major concern for David Moyes, but their attacking woes are.
Beto and Thierno Barry - the Everton's two recognised strikers - had netted just one league goal combined before Sunday's match.
And they were failed to add to that poor tally on a damp and dreary evening on in Liverpool.
Beto's performance was epitomized when he chose to bicycle-kick a golden opportunity from near the goal, despite having room and time to readjust for a more conventional attempt that would have challenged the keeper.
Barry, too, was unable to influence the game after replacing Beto in the second half.
It wasn't for a shortage of chance. The majority of Everton's attacks came through Grealish and the forward, who tirelessly whipped dangerous balls into the Spurs penalty area.
The Toffees: The team head to Sunderland in the Premier League on Monday, 3 November at 8 PM.
Spurs: The London club travel to St James' Park on Wednesday, 29 October for their fourth-round League Cup tie against the Magpies.
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