Micky van de Ven Brace Ends Everton's Run at Brand New Stadium
The Dutch defender became the initial backline player to score two goals in a English top-flight match for Spurs since Jan Vertonghen in spring 2013.
Match summary
The Spurs defender heads into the net twice in first half
The home side's defender has equalizer disallowed after video check
Pape Matar Sarr nets third in 89th minute
The defeat is Everton's initial at Hill Dickinson Stadium
The Tottenham defender scored on two occasions as Spurs extended their unbeaten run on the road in the Premier League and delivered Everton 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 left their historic home behind after 133 years at the end of the previous campaign.
But Tottenham's leader the Dutchman struck on two occasions from corners in the first half to place their impressive record at jeopardy, and they were failed to turn it around before the midfielder - set up by former Toffees attacker the Brazilian - nodded in a final goal to put the game to bed.
The Everton defender thought he had levelled the tally five minutes after Van de Ven's opener, glancing a powerful header past the Spurs keeper from an set-piece.
The Portuguese striker, in the meantime, failed to convert a number of opportunities, while Vicario made a succession of fine saves to ensure the London club went five away games unbeaten in the Premier League.
But the video assistant referee stepped in, instructing Craig Pawson to check the score on the screen and the official ruled that Jack Grealish and the attacker were in offside positions and had impeded with the Spurs keeper.
This victory elevates the manager's side up to third in the Premier League, five points off local foes and leaders Arsenal.
Everton stay 14th and are half a dozen points clear of the drop zone.
Spurs breakdown: Van de Ven excels in duties at each end of the field
After a drab midweek display in the European competition against the French side, where they managed a mere two shots on target, Frank chose the French striker up front instead of ex-Everton forward the Brazilian.
The summer signing was unable to influence the game before being replaced for Richarlison after an hour on the field, but it turns out he proved unnecessary in the final outcome.
Defender Van de Ven converted into an offensive threat to be feared.
Tottenham's first goal came from a cleverly executed corner routine, with the midfielder heading the ball toward the six-yard box for an free the defender to score.
And the captain - stepping up as captain in Cristian Romero's unavailability - added his second in added time as he outjumped Jordan Pickford to nod in.
The Dutchman was just as impressive in defensive duties, partnering well with Kevin Danso as the pair dealt superbly with the 34 crosses thrown their way by the opposition.
Everton analysis: Toffees lacking finishing touch
The club's new home had been a fortress, but it seems the freshness may have worn off somewhat and fans headed to the gates after Sarr's third for Tottenham.
The end in Everton's winning streak at home won't be a major concern for the manager, but their attacking woes are.
The forward and the other striker - the Toffees' pair of established centre-forwards - had scored only a single goal combined before Sunday's outing.
And they were unable to add to that miserable record on a damp and dreary evening on in Liverpool.
The striker's performance was epitomized when he chose to bicycle-kick a clear chance from close range, even with having room and opportunity to reposition for a more conventional attempt that would have challenged the keeper.
Barry, too, failed to influence the game after replacing the starter in the 65th minute.
It wasn't for a shortage of chance. The majority of Everton's offensive moves came through Grealish and the forward, who tirelessly whipped threatening crosses into the Spurs box.
What next for these two sides?
The Toffees: Moyes' men head to the Stadium of Light in the Premier League on Monday, 3 November at 20:00 GMT.
Tottenham: Spurs go to Newcastle's ground on Wednesday, 29 October for their next round Carabao Cup tie against Newcastle.