The Dutch defender became the first defender to net two goals in a Premier League match for Tottenham since the Belgian defender in March 2013.
Match summary
Micky Van de Ven nods into the net twice in opening period
Everton's defender has goal disallowed after video check
Senegalese midfielder nets third in dying moments
This loss is Everton's first at their new ground
Micky van de Ven scored twice as Spurs prolonged their winning streak in away games in the Premier League and delivered Everton their first defeat 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 more than a century at the conclusion of the previous campaign.
But Tottenham's leader the Dutchman pounced twice from set-pieces in the first half to put their strong form at jeopardy, and they were unable to mount a comeback before Pape Matar Sarr - assisted by ex-Everton forward Richarlison - headed home a third to seal the victory.
Jake O'Brien thought he had equalized the tally a short while after Van de Ven's first goal, directing a powerful header past the Spurs keeper from an Everton corner.
Beto, in the meantime, failed to convert a handful of opportunities, while Vicario made a series of fine stops to guarantee Tottenham went five away games unbeaten in the English top flight.
But the video assistant referee stepped in, instructing the match official to review the score on the screen and the referee decided that Jack Grealish and the attacker were in offside positions and had impeded with the Spurs keeper.
The win moves Thomas Frank's side up to third in the division, five points off north London rivals and table-toppers the Gunners.
The Merseyside club remain 14th and sit half a dozen points clear of the drop zone.
After a drab weekday performance in the Champions League against the French side, where they managed a mere two shots on goal, the manager opted for Randal Kolo Muani in attack instead of ex-Everton forward Richarlison.
The summer signing was failed to make much of an impact before being replaced for the substitute after 60 minutes on the field, but it turns out he proved unnecessary in the final outcome.
Centre-back Van de Ven converted into an attacking force to be feared.
Tottenham's opening strike came from a well-worked set-piece play, with Rodrigo Bentancur directing the ball back across the face of goal for an unmarked Van de Ven to head home.
And Ven de Ven - stepping up as captain in the Argentine's absence - added his next goal in first-half stoppage time as he rose above the England keeper to head home.
Van de Ven was equally outstanding in defensive duties, partnering well with Kevin Danso as the duo handled superbly with the numerous deliveries sent their way by Everton.
Everton's recent stadium had been a happy hunting ground, but it seems the freshness may have faded slightly and fans headed to the gates after Sarr's final goal for Spurs.
The end in Everton's winning streak at home won't be a major worry for the manager, but their striker situation are.
The forward and the other striker - the Everton's pair of established strikers - had netted only one league 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.
Beto's form was epitomized when he opted to bicycle-kick a clear chance from near the goal, despite having room and opportunity to readjust for a simpler attempt that would have tested Vicario.
Barry, as well, failed to make an impact after replacing the starter in the second half.
It was not for a shortage of opportunity. Most of the home side's offensive moves came through the winger and Ndiaye, who relentlessly whipped dangerous balls into the Tottenham box.
Everton: The team travel to the Stadium of Light in the top flight on Monday, 3 November at 20:00 GMT.
Spurs: Spurs travel to Newcastle's ground on late October for their fourth-round League Cup match against the Magpies.