The Dutch defender emerged as the initial backline player to score twice in a Premier League match for Tottenham since the Belgian defender in spring 2013.
At a glance
The Spurs defender nods into the net twice in opening period
The home side's Jake O'Brien has goal disallowed after VAR review
Pape Matar Sarr nets final goal in 89th minute
The defeat is Everton's first at their new ground
Micky van de Ven scored on two occasions as Tottenham prolonged their winning streak in away games in the top division and delivered the Toffees their first defeat at their new home.
Everton were undefeated in their last five matches at their recently opened stadium at the dockside location, having departed Goodison Park behind after 133 years at the end of last season.
But Tottenham's leader Van de Ven pounced on two occasions from set-pieces in the first half to place their impressive record at jeopardy, and they were failed to mount a comeback before the midfielder - assisted by ex-Everton forward Richarlison - headed home a final goal to seal the victory.
The Everton defender thought he had levelled the scores five minutes after Van de Ven's opener, directing a powerful header past the Spurs keeper from an set-piece.
The Portuguese striker, meanwhile, missed a number of opportunities, while Vicario made a succession of fine stops to guarantee Tottenham went five away games unbeaten in the English top flight.
But the video assistant referee intervened, instructing Craig Pawson to review the score on the screen and the official ruled that Jack Grealish and the attacker were in an illegal position and had impeded with the Spurs keeper.
The win moves Thomas Frank's team up to third in the Premier League, five points off local foes and leaders Arsenal.
Everton remain in 14th position and are six points clear of the relegation zone.
Following a uninspiring midweek display in the Champions League against Monaco, where they mustered a mere two shots on target, the manager chose the French striker in attack instead of former Toffees player the Brazilian.
The summer signing was unable to make much of an impact before being replaced for Richarlison after an hour on the field, but it turns out he wasn't needed in the final outcome.
Centre-back the Dutchman converted into an attacking force to be feared.
Tottenham's first goal came from a cleverly executed corner routine, with the midfielder heading the ball back across the face of goal for an unmarked Van de Ven to head home.
And the captain - filling in as captain in Cristian Romero's absence - notched his second in first-half stoppage time as he outjumped Jordan Pickford to nod in.
The Dutchman was equally impressive in defence, combining well with Kevin Danso as the pair handled excellently with the numerous deliveries sent their way by Everton.
The club's recent stadium had been a happy hunting ground, but it appears the freshness may have worn off somewhat and fans flocked to the gates after Sarr's final goal for Tottenham.
The break in the team's unbeaten home run won't be a massive worry for David Moyes, but their striker situation are.
The forward and Thierno Barry - the Everton's two established centre-forwards - had scored only one league goal between them before the weekend's match.
And they were failed to contribute to that miserable record on a wet and gloomy evening on Merseyside.
The striker's performance was summed up when he chose to overhead kick a golden opportunity from near the goal, even with having room and opportunity to reposition for a more conventional shot that would have tested the keeper.
The substitute, as well, was unable to make an impact after coming on for Beto in the 65th minute.
It was not for a lack of chance. The majority of Everton's offensive moves came through Grealish and Ndiaye, who relentlessly whipped dangerous crosses into the Spurs penalty area.
The Toffees: Moyes' men travel to Sunderland in the Premier League on early November at 8 PM.
Tottenham: Spurs travel to Newcastle's ground on late October for their next round Carabao Cup tie against Newcastle.
Award-winning journalist with over 15 years of experience covering international affairs and political developments across Europe.