The Dutch defender emerged as the initial backline player to score two goals in a Premier League game for Tottenham since Jan Vertonghen in March 2013.
At a glance
Micky Van de Ven nods into the net two times in first half
Everton's defender has goal ruled after VAR review
Senegalese midfielder scores third in dying moments
The defeat is the Merseyside club's initial at Hill Dickinson Stadium
Micky van de Ven scored twice as Tottenham extended their unbeaten run in away games in the top division and delivered Everton their first defeat at their new home.
Everton were undefeated in their last five matches at their recently opened stadium at Bramley-Moore Dock, having departed their historic home behind after 133 years at the end of the previous campaign.
But Spurs captain the Dutchman pounced on two occasions from set-pieces in the opening 45 minutes to put their strong form at risk, and they were failed to mount a comeback before the midfielder - assisted by former Toffees attacker the Brazilian - headed home a final goal to seal the victory.
The Everton defender believed he had levelled the scores five minutes after the defender's first goal, directing a powerful header past Guglielmo Vicario from an Everton corner.
Beto, meanwhile, missed a number of chances, while the Italian goalkeeper made a succession of excellent saves to ensure the London club went five away games without defeat in the Premier League.
But the video assistant referee stepped in, instructing the match official to check the goal on the pitchside monitor and the referee decided that Jack Grealish and Iliman Ndiaye were in offside positions and had interfered with the Tottenham goalkeeper.
The win moves Thomas Frank's team into third place in the division, a handful of points off local foes and leaders Arsenal.
The Merseyside club remain in 14th position and sit six points ahead of the drop zone.
After a uninspiring midweek performance in the Champions League against Monaco, where they mustered a only two shots on target, the manager chose Randal Kolo Muani in attack instead of former Toffees player Richarlison.
The summer signing was failed to influence the game before being substituted for the substitute after an hour on the field, but it turns out he proved unnecessary in the final outcome.
Centre-back the Dutchman converted into an offensive threat to be reckoned with.
Tottenham's opening strike came from a well-worked set-piece play, with Rodrigo Bentancur heading the ball back across the six-yard box for an unmarked Van de Ven to head home.
And Ven de Ven - stepping up as skipper in Cristian Romero's absence - notched his next goal in first-half stoppage time as he outjumped Jordan Pickford to head home.
The Dutchman was just as outstanding in defence, combining effectively with his defensive colleague as the duo dealt excellently with the numerous deliveries thrown their way by the opposition.
Everton's new home had been a fortress, but it seems the novelty may have worn off slightly and supporters headed to the gates after the midfielder's third for Spurs.
The end in Everton's unbeaten home run will not be a massive concern for David Moyes, but their striker situation will be.
The forward and Thierno Barry - the Everton's pair of established strikers - had scored only a single goal combined before Sunday's match.
And they were unable to add to that poor record on a wet and gloomy night on Merseyside.
Beto's form was summed up when he chose to bicycle-kick a clear chance from close range, even with having room and opportunity to reposition for a more conventional shot that would have tested Vicario.
The substitute, too, was unable to make an impact after coming on for the starter in the 65th minute.
It wasn't for a shortage of chance. The majority of Everton's offensive moves came through the winger and Ndiaye, who tirelessly delivered threatening balls into the Tottenham penalty area.
The Toffees: The team travel to Sunderland in the top flight on Monday, 3 November at 8 PM.
Tottenham: The London club travel to St James' Park on late October for their next round League Cup match against the Magpies.
Loopbaancoach en psycholoog met 15 jaar ervaring in carrièrebegeleiding.