Micky van de Ven Double Halts Everton's Run at New Home Ground
Micky van de Ven emerged as the initial defender to score twice in a English top-flight game for Spurs since Jan Vertonghen in March 2013.
Match summary
The Spurs defender heads into the net two times in opening period
Everton's defender has goal ruled after VAR review
Senegalese midfielder scores final goal in dying moments
The defeat is Everton's first at Hill Dickinson Stadium
The Tottenham defender found the net twice as Tottenham prolonged their winning streak in away games in the top division and delivered the Toffees their initial loss at their new home.
Everton were undefeated in their last five matches at their new ground at the dockside location, having left their historic home behind after 133 years at the conclusion of the previous campaign.
But Tottenham's leader the Dutchman pounced twice from corners in the opening 45 minutes to put their strong form at jeopardy, and they were failed to mount a comeback before Pape Matar Sarr - set up by former Toffees attacker Richarlison - headed home a third to seal the victory.
The Everton defender believed he had levelled the scores five minutes after the defender's first goal, glancing a bullet header past the Spurs keeper from an set-piece.
Beto, meanwhile, failed to convert a number of opportunities, while Vicario made a series of fine stops to ensure Tottenham went five matches on the road unbeaten in the English top flight.
But the video assistant referee intervened, advising Craig Pawson to check the score on the screen and the referee decided that the winger and Iliman Ndiaye were in an illegal position and had impeded with the Tottenham goalkeeper.
This victory moves the manager's side into third place in the division, five points off north London rivals and table-toppers the Gunners.
The Merseyside club remain in 14th position and sit half a dozen points ahead of the drop zone.
Tottenham analysis: Van de Ven fulfils duties at each end of pitch
After a drab weekday display in the European competition against the French side, where they mustered a only two shots on goal, 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 60 minutes on the pitch, but it turns out he wasn't needed in the final outcome.
Defender the Dutchman transformed into an attacking force to be reckoned with.
Tottenham's opening strike came from a well-worked corner routine, with the midfielder directing the ball back across the face of goal for an free Van de Ven to head home.
And the captain - filling in as captain in Cristian Romero's unavailability - added his next goal in first-half stoppage time as he rose above Jordan Pickford to head home.
The Dutchman was just as outstanding in defence, partnering effectively with Kevin Danso as the pair dealt excellently with the numerous deliveries sent their way by Everton.
Toffees breakdown: Toffees missing striker's instinct
Everton's recent stadium had been a fortress, but it appears the novelty may have faded slightly and fans flocked to the gates after Sarr's third for Spurs.
The end in Everton's unbeaten home run will not be a massive worry for the manager, but their striker situation are.
Beto and Thierno Barry - the Toffees' two recognised centre-forwards - had netted only a single goal between them before Sunday's match.
And they were failed to contribute to that poor tally on a wet and gloomy night on in Liverpool.
The striker's performance was epitomized when he opted to bicycle-kick a golden opportunity from near the goal, even with having room and time to reposition for a more conventional shot that would have tested the keeper.
The substitute, too, was unable to influence the game after coming on for Beto in the second half.
It was not for a lack of chance. The majority of Everton's attacks came through the winger and the forward, who relentlessly delivered dangerous balls into the Tottenham penalty area.
What next for these two sides?
The Toffees: Moyes' men head to the Stadium of Light in the Premier League on early November at 20:00 GMT.
Tottenham: Spurs go to St James' Park on Wednesday, 29 October for their fourth-round League Cup match against the Magpies.