Micky van de Ven Double Halts The Toffees' Run at Brand New Home Ground
The Dutch defender emerged as the initial backline player to score two goals in a English top-flight match for Spurs since Jan Vertonghen in March 2013.
At a glance
Micky Van de Ven heads home two times in first half
The home side's defender has equalizer ruled after video check
Senegalese midfielder scores final goal in dying moments
This loss is the Merseyside club's first at their new ground
The Tottenham defender found the net twice as Tottenham extended their winning streak in away games in the top division and handed the Toffees their initial loss at Hill Dickinson Stadium.
The Toffees were unbeaten in their five previous fixtures at their recently opened stadium at Bramley-Moore Dock, having left their historic home behind after 133 years at the conclusion of last season.
But Spurs captain Van de Ven pounced on two occasions from set-pieces in the opening 45 minutes to put their strong form at risk, and they were failed to turn it around before Pape Matar Sarr - assisted by ex-Everton forward Richarlison - nodded in a third to seal the victory.
Jake O'Brien believed he had levelled the tally five minutes after Van de Ven's first goal, glancing a powerful header past Guglielmo Vicario from an set-piece.
Beto, meanwhile, missed a number of opportunities, while the Italian goalkeeper made a succession of excellent saves to ensure Tottenham went five away games without defeat in the English top flight.
But the video assistant referee stepped in, instructing Craig Pawson to check the score on the pitchside monitor and the referee decided that Jack Grealish and the attacker were in an illegal position and had impeded with the Tottenham goalkeeper.
This victory moves Thomas Frank's team into third place in the division, a handful of points off north London rivals and leaders the Gunners.
The Merseyside club stay 14th and are six points clear of the relegation zone.
Tottenham analysis: Van de Ven excels in role at both ends of pitch
After a uninspiring weekday performance in the Champions League against the French side, where they mustered a mere two shots on goal, Frank opted for the French striker in attack instead of ex-Everton forward Richarlison.
The new arrival was unable to influence the game before being replaced for the substitute after an hour on the pitch, but it emerged he wasn't needed in the end.
Defender the Dutchman converted into an attacking force to be feared.
Tottenham's opening strike came from a cleverly executed corner routine, with the midfielder directing the ball toward the six-yard box for an unmarked the defender to head home.
And Ven de Ven - stepping up as captain in Cristian Romero's unavailability - added his next goal in first-half stoppage time as he outjumped the England keeper to head home.
Van de Ven was equally impressive in defensive duties, partnering well with his defensive colleague as the duo dealt superbly with the numerous deliveries thrown their way by Everton.
Everton analysis: Toffees missing finishing touch
Everton's recent stadium had been a fortress, but it appears the novelty may have faded somewhat and fans headed to the gates after the midfielder's third for Spurs.
The end in Everton's winning streak at home won't be a major worry for David Moyes, but their striker situation will be.
The forward and the other striker - the Everton's two recognised centre-forwards - had scored only one league goal between them before the weekend's match.
And they were unable to add to that miserable tally on a damp and dreary night on Merseyside.
The striker's performance was epitomized when he opted to bicycle-kick a clear chance from close range, despite having space and opportunity to reposition for a simpler attempt that would have challenged Vicario.
The substitute, as well, failed to make an impact after replacing Beto in the 65th minute.
It wasn't for a shortage of opportunity. Most of Everton's offensive moves came through Grealish and the forward, who relentlessly delivered threatening crosses into the Spurs box.
What next for these two sides?
Everton: Moyes' men head to Sunderland in the Premier League on early November at 20:00 GMT.
Tottenham: The London club go to Newcastle's ground on Wednesday, 29 October for their fourth-round League Cup tie against Newcastle.