Micky van de Ven Double Halts The Toffees' Run at Brand New Stadium
The Dutch defender emerged as the first backline player to net two goals in a Premier League game for Spurs since the Belgian defender in spring 2013.
At a glance
The Spurs defender heads into the net twice in first half
Everton's defender has goal disallowed after VAR review
Senegalese midfielder nets final goal in 89th minute
The defeat is the Merseyside club's initial at Hill Dickinson Stadium
The Tottenham defender found the net twice 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 five previous fixtures at their new ground at Bramley-Moore Dock, having left their historic home behind after 133 years at the end of the previous campaign.
But Tottenham's leader the Dutchman pounced on two occasions from set-pieces in the opening 45 minutes to place their impressive record at jeopardy, and they were unable to turn it around before the midfielder - assisted by former Toffees attacker Richarlison - nodded in a final goal to seal the victory.
Jake O'Brien thought he had levelled the tally a short while after the defender's opener, directing a powerful header past the Spurs keeper from an Everton corner.
Beto, in the meantime, failed to convert a number of chances, while Vicario made a series of fine saves to guarantee Tottenham went five matches on the road without defeat in the English top flight.
But the VAR stepped in, advising Craig Pawson to check the goal on the screen and the official decided that the winger and Iliman Ndiaye were in an illegal position and had interfered with the Spurs keeper.
The win moves Thomas Frank's team into third place in the Premier League, a handful of points off north London rivals and leaders Arsenal.
Everton remain 14th and sit half a dozen points clear of the drop zone.
Tottenham analysis: Van de Ven excels in duties at both ends of the field
Following a uninspiring weekday display in the European competition against the French side, where they mustered a mere two shots on target, the manager chose the French striker up front instead of former Toffees player the Brazilian.
The summer signing was unable to make much of an impact before being replaced for Richarlison after 60 minutes on the field, but it turns out he wasn't needed in the end.
Defender Van de Ven transformed into an offensive threat to be feared.
Tottenham's first goal came from a well-worked set-piece play, with the midfielder directing the ball back across the six-yard box for an free the defender to score.
And Ven de Ven - filling in as captain in the Argentine's unavailability - added his next goal in first-half stoppage time as he rose above the England keeper to nod in.
Van de Ven was equally outstanding in defence, combining well with Kevin Danso as the duo dealt excellently with the numerous deliveries sent their way by the opposition.
Toffees breakdown: Everton missing striker's instinct
Everton's recent stadium had been a happy hunting ground, but it appears the freshness may have worn off somewhat and fans headed to the gates after the midfielder's final goal for Spurs.
The end in the team's unbeaten home run will not be a major worry for the manager, but their striker situation are.
The forward and the other striker - the Toffees' two established centre-forwards - had netted just a single goal combined before the weekend's match.
And they were unable to contribute to that poor record on a wet and gloomy evening on Merseyside.
Beto's form was epitomized 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 Vicario.
The substitute, too, failed to make an impact after replacing Beto in the second half.
It wasn't for a lack of chance. Most of Everton's attacks came through Grealish and the forward, who relentlessly whipped threatening balls into the Tottenham box.
Upcoming fixtures for both teams?
The Toffees: Moyes' men travel to Sunderland in the Premier League on Monday, 3 November at 20:00 GMT.
Tottenham: The London club go to St James' Park on Wednesday, 29 October for their next round Carabao Cup tie against Newcastle.