The Dutch defender emerged as the initial backline player to score two goals in a English top-flight match for Tottenham since the Belgian defender in spring 2013.
Match summary
Micky Van de Ven nods home twice in first half
Everton's Jake O'Brien has equalizer ruled after video check
Senegalese midfielder scores final goal in dying moments
This loss is the Merseyside club's first at their new ground
The Tottenham defender scored on two occasions as Spurs prolonged their winning streak on the road in the Premier League and handed Everton their first defeat at their new home.
The Toffees were unbeaten in their five previous fixtures at their new ground at Bramley-Moore Dock, having departed Goodison Park behind after 133 years at the conclusion of last season.
But Tottenham's leader Van de Ven pounced twice from corners in the first half to put their impressive record at jeopardy, and they were unable to mount a comeback before Pape Matar Sarr - set up by former Toffees attacker the Brazilian - nodded in a third to seal the victory.
The Everton defender thought he had equalized the scores five minutes after the defender's opener, directing a powerful header past the Spurs keeper from an Everton corner.
Beto, meanwhile, missed a handful of opportunities, while Vicario made a succession of fine saves to ensure Tottenham went five away games without defeat in the English top flight.
But the VAR stepped in, instructing Craig Pawson to review the score on the pitchside monitor and the referee decided that the winger and the attacker were in an illegal position and had interfered with the Tottenham goalkeeper.
The win elevates Thomas Frank's team into third place in the Premier League, a handful of points off north London rivals and leaders Arsenal.
Everton remain in 14th position and sit half a dozen points clear of the drop zone.
Following a uninspiring weekday display in the European competition against Monaco, where they mustered a mere two shots on goal, Frank opted for the French striker in attack instead of former Toffees player Richarlison.
The new arrival was failed to make much of an impact before being substituted for the substitute after an hour on the pitch, but it emerged he wasn't needed in the end.
Centre-back the Dutchman transformed into an attacking force to be feared.
Spurs' first goal came from a cleverly executed set-piece play, with the midfielder 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 skipper in the Argentine's unavailability - added his next goal in added time as he rose above Jordan Pickford to nod in.
Van de Ven was equally outstanding in defence, partnering effectively with Kevin Danso as the duo handled superbly with the 34 crosses thrown their way by the opposition.
Everton's recent stadium had been a happy hunting ground, but it appears the novelty may have faded slightly and fans flocked to the gates after Sarr's third for Spurs.
The break in the team's unbeaten home run will not be a major concern for the manager, but their striker situation are.
The forward and Thierno Barry - the Everton's two established centre-forwards - had scored just a single goal combined before Sunday's outing.
And they were failed to contribute to that miserable record on a damp and dreary evening on Merseyside.
Beto's performance was summed up when he opted to overhead kick a clear chance from close range, even with having space and time to readjust for a more conventional shot that would have tested the keeper.
Barry, as well, was unable to make an impact after replacing the starter in the 65th minute.
It was not for a lack of chance. The majority of Everton's offensive moves came through the winger and Ndiaye, who tirelessly whipped threatening crosses into the Spurs box.
The Toffees: The team head to the Stadium of Light in the Premier League on Monday, 3 November at 8 PM.
Tottenham: The London club travel to Newcastle's ground on late October for their next round League Cup match against the Magpies.