Micky van de Ven Brace Ends Everton's Run at New Home Ground
The Dutch defender emerged as the first backline player to net twice in a English top-flight game for Tottenham since Jan Vertonghen in spring 2013.
Match summary
Micky Van de Ven nods into the net two times in first half
Everton's Jake O'Brien has goal disallowed after VAR review
Senegalese midfielder nets third in 89th minute
This loss is the Merseyside club's first at Hill Dickinson Stadium
The Tottenham defender scored on two occasions as Spurs extended their unbeaten run on the road in the top division and handed the Toffees their initial loss at their new home.
The Toffees were unbeaten in their last five matches at their new ground at the dockside location, having departed Goodison Park behind after 133 years at the end of last season.
But Tottenham's leader Van de Ven struck twice from set-pieces in the first half to place their impressive record at jeopardy, and they were failed to turn it around before the midfielder - assisted by ex-Everton forward the Brazilian - headed home a final goal to seal the victory.
Jake O'Brien believed he had levelled the tally a short while after Van de Ven's opener, glancing a powerful header past Guglielmo Vicario from an Everton corner.
Beto, meanwhile, missed a number of opportunities, while the Italian goalkeeper made a series of excellent stops to guarantee Tottenham went five matches on the road unbeaten in the Premier League.
But the video assistant referee stepped in, instructing the match official to check the score on the screen and the official decided that Jack Grealish and the attacker were in offside positions and had impeded with the Spurs keeper.
This victory moves the manager's side up to third in the division, five points off north London rivals and leaders the Gunners.
Everton remain in 14th position and are half a dozen points clear of the drop zone.
Spurs breakdown: Van de Ven excels in role at both ends of the field
After a uninspiring weekday display in the European competition against Monaco, where they managed a mere attempts on goal, Frank opted for the French striker up front instead of former Toffees player Richarlison.
The summer signing was unable to make much of an impact before being substituted for the substitute after an hour on the field, but it emerged he wasn't needed in the final outcome.
Centre-back the Dutchman converted into an offensive threat to be reckoned with.
Tottenham's first goal came from a cleverly executed set-piece play, with Rodrigo Bentancur heading the ball back across the six-yard box for an unmarked the defender to score.
And the captain - filling in as skipper in the Argentine's absence - notched his second in added time as he outjumped the England keeper to nod in.
The Dutchman was equally impressive in defensive duties, combining effectively with Kevin Danso as the pair dealt superbly with the numerous deliveries thrown their way by the opposition.
Toffees breakdown: Everton lacking finishing touch
Everton's recent stadium had been a fortress, but it seems the freshness may have worn off slightly and fans headed to the gates after the midfielder's third for Tottenham.
The break in Everton's unbeaten home run won't be a massive worry for David Moyes, but their attacking woes will be.
Beto and the other striker - the Everton's two recognised strikers - had netted only one league goal between them before the weekend's match.
And they were failed to add to that poor tally on a wet and gloomy evening on in Liverpool.
Beto's form was summed up when he opted to bicycle-kick a clear chance from close range, even with having space and opportunity to reposition for a more conventional shot that would have challenged the keeper.
Barry, as well, was unable to make an impact after coming on for Beto in the second half.
It wasn't for a shortage of opportunity. Most of the home side's attacks came through Grealish and Ndiaye, who relentlessly whipped threatening crosses into the Spurs penalty area.
What next for both teams?
The Toffees: The team travel to the Stadium of Light in the Premier League on early November at 20:00 GMT.
Tottenham: Spurs go to Newcastle's ground on Wednesday, 29 October for their fourth-round Carabao Cup tie against the Magpies.