Micky van de Ven Double Ends Everton's Run at Brand New Home Ground
The Dutch defender emerged as the first defender to net two goals in a English top-flight match for Spurs since Jan Vertonghen in spring 2013.
Match summary
Micky Van de Ven heads into the net two times in opening period
The home side's defender has goal disallowed after video check
Senegalese midfielder nets third in 89th minute
The defeat is Everton's initial at Hill Dickinson Stadium
Micky van de Ven found the net on two occasions as Spurs prolonged their unbeaten run in away games in the top division and handed Everton their first defeat at their new home.
The Toffees were unbeaten 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 the Dutchman struck twice from set-pieces in the opening 45 minutes to put their impressive record at jeopardy, and they were failed to turn it around before Pape Matar Sarr - set up by ex-Everton forward the Brazilian - nodded in a final goal to seal the victory.
Jake O'Brien thought he had levelled the scores five minutes 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 series of excellent stops to ensure the London club went five matches on the road without defeat in the Premier League.
But the video assistant referee stepped in, instructing Craig Pawson to review the score on the screen and the official ruled that the winger and the attacker were in offside positions and had impeded with the Tottenham goalkeeper.
This victory moves Thomas Frank's side up to third in the Premier League, a handful of points off north London rivals and leaders the Gunners.
Everton remain in 14th position and are six points ahead of the relegation zone.
Spurs breakdown: Van de Ven excels in role at both ends of the field
Following a drab midweek display in the European competition against Monaco, where they mustered a mere two shots on goal, the manager opted for Randal Kolo Muani in attack instead of former Toffees player the Brazilian.
The new arrival was failed to influence the game before being replaced for the substitute after 60 minutes on the field, but it emerged he proved unnecessary in the end.
Defender Van de Ven converted into an offensive threat to be feared.
Spurs' first goal came from a cleverly executed set-piece play, with the midfielder directing the ball toward the six-yard box for an unmarked the defender to score.
And Ven de Ven - filling in as skipper in the Argentine's unavailability - added his second in first-half stoppage time as he rose above Jordan Pickford to head home.
The Dutchman was equally impressive in defensive duties, partnering well with Kevin Danso as the pair handled superbly with the numerous deliveries thrown their way by the opposition.
Toffees breakdown: Toffees missing finishing touch
The club's recent stadium had been a happy hunting ground, but it seems the novelty may have faded slightly and supporters flocked to the gates after Sarr's third for Tottenham.
The break in the team's winning streak at home won't be a major worry for David Moyes, but their attacking woes are.
Beto and the other striker - the Everton's two established centre-forwards - had netted only a single goal combined before Sunday's outing.
And they were failed to contribute to that miserable tally on a wet and gloomy evening on in Liverpool.
The striker's performance was epitomized when he opted to bicycle-kick a golden opportunity from near the goal, despite having room and time to reposition for a more conventional shot that would have tested Vicario.
The substitute, as well, failed to influence the game after coming on for Beto in the second half.
It was not for a shortage of opportunity. Most of Everton's attacks came through Grealish and Ndiaye, who relentlessly whipped threatening crosses into the Spurs penalty area.
What next for these two sides?
Everton: The team travel to the Stadium of Light in the Premier League on early November at 20:00 GMT.
Spurs: Spurs go to Newcastle's ground on late October for their next round Carabao Cup match against the Magpies.