Micky van de Ven Brace Ends The Toffees' Run at Brand New Stadium
The Dutch defender emerged as the first backline player to score two goals in a Premier League match for Spurs since Jan Vertonghen in spring 2013.
Match summary
The Spurs defender nods into the net two times in first half
The home side's Jake O'Brien has equalizer disallowed after video check
Pape Matar Sarr nets final goal in 89th minute
The defeat is Everton's first at Hill Dickinson Stadium
The Tottenham defender found the net twice as Spurs prolonged their unbeaten run in away games in the Premier League and delivered Everton their first defeat at their new home.
Everton were unbeaten 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 last season.
But Spurs captain Van de Ven struck on two occasions from set-pieces in the opening 45 minutes to place their impressive record at jeopardy, and they were failed to mount a comeback before the midfielder - set up by ex-Everton forward the Brazilian - headed home a third to seal the victory.
The Everton defender thought he had levelled the scores a short while after Van de Ven's first goal, directing a powerful header past the Spurs keeper from an Everton corner.
Beto, meanwhile, missed a number of opportunities, while Vicario made a succession of fine saves to ensure Tottenham went five matches on the road without defeat in the English top flight.
But the video assistant referee intervened, instructing Craig Pawson to check the goal on the pitchside monitor and the referee decided that Jack Grealish and the attacker were in offside positions and had interfered with the Tottenham goalkeeper.
This victory moves the manager's team into third place in the Premier League, five points off local foes and table-toppers the Gunners.
Everton stay in 14th position and are six points clear of the relegation zone.
Spurs breakdown: Van de Ven excels in duties at each end of pitch
Following a drab weekday performance in the European competition against the French side, where they managed a mere attempts on target, Frank chose the French striker in attack instead of ex-Everton forward the Brazilian.
The new arrival was failed to make much of an impact before being replaced for the substitute after an hour on the pitch, but it turns out he wasn't needed in the final outcome.
Centre-back the Dutchman converted into an attacking force to be feared.
Spurs' first goal came from a well-worked set-piece play, with the midfielder heading the ball toward the face of goal for an free the defender to head home.
And the captain - stepping up as captain in the Argentine's unavailability - added his second in first-half stoppage time as he rose above the England keeper to nod in.
Van de Ven was equally outstanding in defence, partnering effectively with Kevin Danso as the duo dealt superbly with the 34 crosses sent their way by the opposition.
Everton analysis: Everton missing finishing touch
The club's new home had been a happy hunting ground, but it seems the novelty may have worn off slightly and fans headed to the exits after the midfielder's third for Spurs.
The end in the team's unbeaten home run will not be a massive worry for David Moyes, but their attacking woes will be.
Beto and the other striker - the Everton's pair of established strikers - had netted just one league goal between them before the weekend's match.
And they were unable to add to that poor record on a damp and dreary night on in Liverpool.
The striker's form was epitomized when he chose to bicycle-kick a golden opportunity from close range, despite having room and opportunity to readjust for a simpler shot that would have tested the keeper.
Barry, too, failed to make an impact after coming on for the starter in the 65th minute.
It wasn't for a shortage of chance. The majority of the home side's attacks came through Grealish and Ndiaye, who tirelessly delivered threatening balls 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 League Cup match against Newcastle.