The Dutch defender became the initial defender to net twice in a Premier League game for Tottenham since the Belgian defender in March 2013.
At a glance
Micky Van de Ven heads home two times in first half
The home side's Jake O'Brien has equalizer ruled after VAR review
Pape Matar Sarr nets final goal in 89th minute
The defeat is Everton's first at Hill Dickinson Stadium
Micky van de Ven found the net twice as Spurs extended their unbeaten run in away games in the top division and delivered the Toffees their first defeat at Hill Dickinson Stadium.
Everton were unbeaten in their last five matches at their new ground at Bramley-Moore Dock, having left Goodison Park behind after 133 years at the conclusion of last season.
But Spurs captain Van de Ven pounced twice from set-pieces in the first half to place their impressive record at jeopardy, and they were failed to turn it around before Pape Matar Sarr - assisted by former Toffees attacker Richarlison - nodded in a final goal to put the game to bed.
Jake O'Brien thought he had levelled the tally a short while after the defender's first goal, glancing a bullet header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, meanwhile, failed to convert a handful of chances, while the Italian goalkeeper made a series of fine saves to ensure Tottenham went five matches on the road unbeaten in the English top flight.
But the VAR intervened, advising Craig Pawson to check the score on the pitchside monitor and the referee ruled that the winger and the attacker were in offside positions and had interfered with the Spurs keeper.
The win elevates Thomas Frank's side into third place in the division, five points off north London rivals and table-toppers the Gunners.
Everton remain in 14th position and are half a dozen points ahead of the relegation zone.
After a drab weekday performance in the European competition against the French side, where they mustered a mere two shots on target, the manager opted for Randal Kolo Muani 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 field, but it turns out he proved unnecessary in the final outcome.
Defender the Dutchman transformed into an attacking force to be feared.
Spurs' first goal came from a well-worked corner routine, with Rodrigo Bentancur directing the ball toward the six-yard box for an unmarked Van de Ven to head home.
And the captain - stepping up as skipper in Cristian Romero's absence - notched his second in added time as he rose above Jordan Pickford to head home.
Van de Ven was equally outstanding in defence, combining well with his defensive colleague as the pair dealt excellently with the 34 crosses sent their way by the opposition.
Everton's recent stadium had been a fortress, but it seems the freshness may have faded slightly and supporters headed to the exits after the midfielder's third for Spurs.
The end in the team's winning streak at home will not be a major concern for the manager, but their attacking woes will be.
Beto and the other striker - the Toffees' pair of recognised strikers - had netted only a single goal combined before Sunday's match.
And they were unable to contribute to that miserable tally on a wet and gloomy night on in Liverpool.
Beto's performance was summed up when he chose to overhead kick a clear chance from close range, even with having space and opportunity to readjust for a more conventional attempt that would have challenged Vicario.
The substitute, as well, failed to make an impact after replacing the starter in the second half.
It was not for a shortage of chance. Most of Everton's offensive moves came through the winger and Ndiaye, who tirelessly delivered threatening balls into the Spurs penalty area.
The Toffees: Moyes' men head to the Stadium of Light in the top flight on Monday, 3 November at 20:00 GMT.
Spurs: Spurs go to Newcastle's ground on Wednesday, 29 October for their fourth-round Carabao Cup match against the Magpies.
Lucas van der Meer is a digital strategist focused on empowering local economies with technology-driven market solutions.