The Dutch defender became the first defender to net two goals in a Premier League match for Tottenham since Jan Vertonghen in March 2013.
Key points
Micky Van de Ven nods home twice in first half
Everton's Jake O'Brien has equalizer disallowed after video check
Pape Matar Sarr scores final goal in 89th minute
This loss is the Merseyside club's initial at Hill Dickinson Stadium
Micky van de Ven scored twice as Spurs prolonged their unbeaten run in away games in the Premier League and delivered Everton their initial loss at Hill Dickinson Stadium.
The Toffees were undefeated in their five previous fixtures at their new ground at Bramley-Moore Dock, having left Goodison Park behind after 133 years at the conclusion of the previous campaign.
But Spurs captain the Dutchman struck on two occasions from set-pieces in the first half to put their strong form at risk, and they were failed to turn it around before Pape Matar Sarr - set up by former Toffees attacker the Brazilian - nodded in a third to seal the victory.
The Everton defender believed he had equalized the scores five minutes 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 opportunities, while the Italian goalkeeper made a succession of fine stops to guarantee Tottenham went five away games without defeat in the English top flight.
But the video assistant referee stepped in, instructing the match official to review the goal on the pitchside monitor and the referee decided that the winger and Iliman Ndiaye were in offside positions and had impeded with the Tottenham goalkeeper.
This victory elevates Thomas Frank's team up to third in the division, a handful of points off north London rivals and table-toppers the Gunners.
The Merseyside club stay in 14th position and sit six points clear of the drop zone.
After a uninspiring weekday performance in the Champions League against the French side, where they mustered a mere attempts on target, the manager opted for the French striker in attack instead of ex-Everton forward Richarlison.
The summer signing was unable to make much of an impact before being substituted for the substitute after 60 minutes on the pitch, but it turns out he proved unnecessary in the final outcome.
Centre-back Van de Ven converted into an attacking force to be reckoned with.
Tottenham's opening strike came from a well-worked set-piece play, with the midfielder heading the ball toward the six-yard box for an free Van de Ven to head home.
And the captain - stepping up as skipper in the Argentine's absence - added his next goal in first-half stoppage time as he outjumped Jordan Pickford to nod in.
Van de Ven was just as impressive in defensive duties, combining effectively with his defensive colleague as the pair handled excellently with the numerous deliveries sent their way by the opposition.
Everton's recent stadium had been a happy hunting ground, but it appears the freshness may have worn off slightly and fans flocked to the gates after Sarr's third for Spurs.
The end in the team's winning streak at home will not be a major concern for David Moyes, but their attacking woes will be.
The forward and Thierno Barry - the Everton's pair of established strikers - had netted just one league goal combined before Sunday's match.
And they were failed to add to that poor record on a damp and dreary evening on Merseyside.
The striker's performance was summed up when he chose to bicycle-kick a clear chance from near the goal, even with having room and time to readjust for a simpler attempt that would have challenged the keeper.
Barry, as well, was unable to make an impact after replacing the starter in the second half.
It wasn't for a lack of opportunity. Most of the home side's offensive moves came through Grealish and the forward, who relentlessly whipped dangerous balls into the Tottenham penalty area.
The Toffees: Moyes' men travel to Sunderland in the top flight on early November at 8 PM.
Spurs: Spurs travel to Newcastle's ground on Wednesday, 29 October for their next round Carabao Cup match against Newcastle.
Elena is a city lifestyle expert passionate about finding the best urban deals and sharing money-saving tips for metropolitan dwellers.