Micky van de Ven Double Ends The Toffees' Run at New Home Ground
The Dutch defender became the initial defender to score twice in a English top-flight game for Tottenham since Jan Vertonghen in March 2013.
Match summary
Micky Van de Ven nods into the net twice in first half
Everton's Jake O'Brien has equalizer disallowed after VAR review
Pape Matar Sarr scores third in 89th minute
The defeat is the Merseyside club's first at Hill Dickinson Stadium
The Tottenham defender scored twice as Tottenham prolonged their unbeaten run on the road in the Premier League and handed the Toffees their first defeat at their new home.
The Toffees were undefeated 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 the previous campaign.
But Spurs captain Van de Ven pounced on two occasions from set-pieces in the first half to place their strong form at risk, and they were unable to mount a comeback before the midfielder - set up by former Toffees attacker Richarlison - nodded in a third to put the game to bed.
Jake O'Brien believed he had levelled the scores a short while after Van de Ven's opener, directing a powerful header past Guglielmo Vicario from an set-piece.
Beto, meanwhile, failed to convert a number of chances, while the Italian goalkeeper made a succession of excellent saves to ensure Tottenham went five matches on the road unbeaten in the English top flight.
But the VAR intervened, instructing the match official to check the goal on the screen and the official decided that the winger and Iliman Ndiaye were in offside positions and had impeded with the Tottenham goalkeeper.
This victory elevates the manager's side up to third in the Premier League, a handful of points off local foes and table-toppers Arsenal.
Everton stay 14th and sit half a dozen points ahead of the relegation zone.
Spurs breakdown: The defender fulfils role at each end of pitch
Following a drab weekday display in the European competition against Monaco, where they mustered a mere attempts on goal, the manager opted for the French striker in attack instead of ex-Everton forward Richarlison.
The new arrival was unable to influence the game 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 the Dutchman converted into an attacking force to be feared.
Spurs' opening strike came from a cleverly executed corner routine, with the midfielder heading the ball toward the face of goal for an unmarked the defender to score.
And the captain - filling in as captain in the Argentine's absence - added his second in added time as he rose above Jordan Pickford to nod in.
The Dutchman was just as outstanding in defence, combining effectively with Kevin Danso as the duo handled superbly with the numerous deliveries sent their way by Everton.
Everton analysis: Toffees lacking striker's instinct
The club's recent stadium had been a fortress, but it seems the novelty may have worn off slightly and fans headed to the gates after Sarr's third for Spurs.
The end in the team's winning streak at home won't be a major worry for David Moyes, but their striker situation will be.
Beto and Thierno Barry - the Toffees' two established strikers - had netted just one league goal combined before Sunday's outing.
And they were failed to contribute to that poor record on a damp and dreary evening on Merseyside.
The striker's form was summed up when he opted to overhead kick a golden opportunity from close range, even with having room and time to reposition for a simpler attempt that would have tested Vicario.
Barry, too, was unable to influence the game after replacing the starter in the second half.
It wasn't for a lack of opportunity. Most of Everton's attacks came through Grealish and Ndiaye, who tirelessly whipped threatening crosses into the Spurs penalty area.
What next for these two sides?
Everton: Moyes' men head to Sunderland in the Premier League on Monday, 3 November at 8 PM.
Spurs: The London club go to St James' Park on late October for their next round League Cup match against Newcastle.