Micky van de Ven Double Ends The Toffees' Run at New Home Ground
Micky van de Ven became the first backline player to score two goals in a English top-flight game for Tottenham since the Belgian defender in spring 2013.
Match summary
Micky Van de Ven heads into the net twice in first half
Everton's Jake O'Brien has goal disallowed after VAR review
Senegalese midfielder scores final goal in dying moments
The defeat is the Merseyside club's initial at Hill Dickinson Stadium
The Tottenham defender scored twice as Spurs prolonged their winning streak in away games in the Premier League and delivered the Toffees their initial loss at their new home.
The Toffees were unbeaten in their last five matches at their recently opened stadium at Bramley-Moore Dock, having departed their historic home behind after 133 years at the end of last season.
But Spurs captain the Dutchman pounced twice from corners in the opening 45 minutes to place their strong form at jeopardy, and they were unable to turn it around before the midfielder - set up by former Toffees attacker Richarlison - headed home a third to put the game to bed.
Jake O'Brien believed he had levelled the tally a short while after Van de Ven's opener, directing a powerful header past the Spurs keeper from an set-piece.
Beto, in the meantime, failed to convert a number of opportunities, while Vicario made a succession of fine stops to guarantee the London club went five matches on the road without defeat in the English top flight.
But the VAR intervened, advising the match official to review the goal on the pitchside monitor and the official ruled that the winger and Iliman Ndiaye were in offside positions and had impeded with the Tottenham goalkeeper.
This victory elevates Thomas Frank's team up to third in the Premier League, five points off north London rivals and leaders Arsenal.
Everton remain in 14th position and sit six points ahead of the drop zone.
Spurs breakdown: Van de Ven excels in role at each end of the field
Following a uninspiring weekday display in the European competition against Monaco, where they mustered a mere two shots on target, the manager opted for the French striker up front instead of ex-Everton forward Richarlison.
The summer signing was failed to influence the game before being substituted for the substitute after 60 minutes on the pitch, but it turns out he wasn't needed in the final outcome.
Centre-back Van de Ven transformed into an offensive threat to be feared.
Spurs' opening strike came from a well-worked corner routine, with Rodrigo Bentancur heading the ball back across the face of goal for an unmarked the defender to score.
And the captain - stepping up as captain in the Argentine's unavailability - added his next goal in added time as he outjumped Jordan Pickford to head home.
The Dutchman was just as outstanding in defence, partnering effectively with Kevin Danso as the duo dealt excellently with the numerous deliveries sent their way by Everton.
Everton analysis: Everton missing striker's instinct
Everton's new home had been a fortress, but it appears the freshness may have faded slightly and supporters headed to the gates after the midfielder's third for Tottenham.
The break in the team's winning streak at home will not be a major worry for the manager, but their attacking woes will be.
Beto and the other striker - the Toffees' pair of established strikers - had netted just a single goal combined before Sunday's outing.
And they were failed to contribute to that poor tally on a damp and dreary evening on Merseyside.
Beto's form was summed up when he chose to bicycle-kick a golden opportunity from near the goal, even with having space and time to readjust for a more conventional shot that would have challenged the keeper.
The substitute, as well, failed to influence the game after coming on for Beto in the 65th minute.
It wasn't for a shortage of chance. Most of Everton's offensive moves came through the winger and the forward, who tirelessly whipped threatening balls into the Spurs penalty area.
What next for these two sides?
Everton: The team travel to Sunderland in the top flight on Monday, 3 November at 8 PM.
Spurs: Spurs go to Newcastle's ground on late October for their next round League Cup match against Newcastle.