The Dutch defender emerged as the initial backline player to net two goals in a Premier League match for Tottenham since the Belgian defender in March 2013.
Match summary
Micky Van de Ven heads into the net two times in opening period
Everton's defender has goal disallowed after video check
Pape Matar Sarr nets final goal in dying moments
This loss is the Merseyside club's first 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 their new home.
Everton were undefeated in their five previous fixtures at their recently opened stadium at the dockside location, having left their historic home behind after more than a century at the end of last season.
But Tottenham's leader the Dutchman struck twice from corners in the opening 45 minutes to place their impressive record at jeopardy, and they were unable to mount a comeback before the midfielder - assisted by ex-Everton forward Richarlison - nodded in a final goal to put the game to bed.
The Everton defender thought he had equalized the tally a short while after the defender's first goal, glancing a bullet header past Guglielmo Vicario from an Everton corner.
Beto, meanwhile, failed to convert a handful of chances, while Vicario made a succession of excellent stops to ensure Tottenham went five away games unbeaten in the English top flight.
But the video assistant referee intervened, advising the match official to review the goal on the screen and the referee ruled that the winger and the attacker were in offside positions and had impeded with the Spurs keeper.
The win elevates the manager's team up to third in the Premier League, a handful of points off north London rivals and table-toppers Arsenal.
The Merseyside club remain in 14th position and are six points clear of the relegation zone.
After a uninspiring midweek display in the Champions League against the French side, where they managed a mere attempts on target, the manager chose the French striker in attack instead of ex-Everton forward the Brazilian.
The summer signing was unable to influence the game before being substituted for the substitute after 60 minutes on the pitch, but it turns out he proved unnecessary in the final outcome.
Defender the Dutchman transformed into an attacking force to be feared.
Tottenham's first goal came from a cleverly executed set-piece play, with Rodrigo Bentancur heading the ball toward the six-yard box for an free the defender to head home.
And Ven de Ven - filling in as captain in the Argentine's unavailability - added his next goal in first-half stoppage time as he outjumped the England keeper to nod in.
The Dutchman was just as outstanding in defensive duties, partnering effectively with Kevin Danso as the pair handled superbly with the numerous deliveries sent their way by the opposition.
Everton's new home had been a fortress, but it appears the freshness may have worn off slightly and supporters headed to the gates after Sarr's final goal for Spurs.
The break in Everton's unbeaten home run will not be a massive worry for the manager, but their striker situation are.
Beto and Thierno Barry - the Toffees' two established strikers - had scored just a single goal between them before Sunday's outing.
And they were unable to add to that poor tally on a wet and gloomy evening on in Liverpool.
Beto's performance was summed up when he opted to overhead kick a clear chance from close range, even with having room and opportunity to readjust for a more conventional shot that would have challenged the keeper.
Barry, as well, 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 attacks came through Grealish and the forward, who relentlessly whipped dangerous balls into the Spurs penalty area.
The Toffees: The team travel to the Stadium of Light in the Premier League on Monday, 3 November at 8 PM.
Tottenham: Spurs travel to Newcastle's ground on Wednesday, 29 October for their fourth-round Carabao Cup match against Newcastle.
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