Micky van de Ven Brace Halts The Toffees' Run at New Stadium
The Dutch defender became the initial backline player to net twice in a Premier League match for Spurs since the Belgian defender in spring 2013.
Match summary
The Spurs defender heads into the net two times in first half
Everton's defender has equalizer ruled after VAR review
Senegalese midfielder nets third in 89th minute
The defeat is Everton's initial at Hill Dickinson Stadium
Micky van de Ven scored on two occasions as Spurs extended their unbeaten run in away games in the top division and handed the Toffees their first defeat at their new home.
Everton were unbeaten in their five previous fixtures at their new ground at the dockside location, having departed Goodison Park behind after more than a century at the conclusion of last season.
But Tottenham's leader the Dutchman pounced on two occasions from corners in the opening 45 minutes to put their strong form at risk, and they were unable to turn it around before Pape Matar Sarr - assisted by ex-Everton forward Richarlison - nodded in a final goal to seal the victory.
Jake O'Brien thought he had equalized the scores a short while after Van de Ven's first goal, glancing a powerful header past the Spurs keeper from an Everton corner.
Beto, in the meantime, missed a number of opportunities, while Vicario made a succession of fine saves to ensure the London club went five matches on the road unbeaten 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 ruled that the winger and Iliman Ndiaye were in offside positions and had interfered with the Tottenham goalkeeper.
This victory elevates the manager's team into third place in the Premier League, five points off local foes and leaders Arsenal.
The Merseyside club remain in 14th position and sit half a dozen points clear of the relegation zone.
Tottenham analysis: Van de Ven excels in duties at both ends of the field
Following a uninspiring midweek performance in the European competition against the French side, where they managed a only attempts on goal, Frank chose Randal Kolo Muani up front instead of former Toffees player Richarlison.
The new arrival was failed to make much of an impact before being substituted for the substitute after 60 minutes on the pitch, but it emerged he proved unnecessary in the end.
Defender the Dutchman converted into an offensive threat to be reckoned with.
Spurs' first goal came from a well-worked set-piece play, with Rodrigo Bentancur directing the ball toward the face of goal for an free the defender to score.
And the captain - filling in as captain in Cristian Romero's absence - added his next goal in first-half stoppage time as he outjumped Jordan Pickford to nod in.
Van de Ven was just as outstanding in defensive duties, partnering effectively with his defensive colleague as the pair handled superbly with the 34 crosses thrown their way by Everton.
Toffees breakdown: Toffees lacking finishing touch
Everton's recent stadium had been a happy hunting ground, but it seems the freshness may have worn off slightly and fans flocked to the exits after Sarr's third for Tottenham.
The end in Everton's unbeaten home run will not be a major worry for David Moyes, but their attacking woes will be.
The forward and the other striker - the Toffees' pair of established strikers - had netted only one league goal combined before the weekend's match.
And they were unable to contribute to that poor tally on a wet and gloomy night on Merseyside.
Beto's form was epitomized when he opted to bicycle-kick a golden opportunity from close range, even with having room and time to reposition for a simpler shot that would have tested Vicario.
The substitute, as well, failed to make an impact after coming on for Beto in the second half.
It was not for a lack of opportunity. The majority of Everton's offensive moves came through Grealish and Ndiaye, who relentlessly delivered dangerous crosses into the Tottenham penalty area.
What next for both teams?
The Toffees: Moyes' men travel to the Stadium of Light in the Premier League on Monday, 3 November at 20:00 GMT.
Spurs: The London club go to Newcastle's ground on Wednesday, 29 October for their next round Carabao Cup tie against the Magpies.