Micky van de Ven Double Ends Everton's Run at New Stadium
Micky van de Ven emerged as the initial backline player to score twice in a Premier League game for Spurs since the Belgian defender in spring 2013.
At a glance
The Spurs defender heads into the net twice in opening period
The home side's defender has goal disallowed after VAR review
Senegalese midfielder scores third in 89th minute
The defeat is Everton's first at Hill Dickinson Stadium
The Tottenham defender found the net on two occasions as Tottenham prolonged their unbeaten run in away games 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 more than a century at the end of the previous campaign.
But Tottenham's leader the Dutchman struck on two occasions from corners in the opening 45 minutes to place their strong form at jeopardy, and they were unable to mount a comeback before the midfielder - assisted by former Toffees attacker Richarlison - nodded in a final goal to seal the victory.
The Everton defender thought he had levelled the tally a short while after the defender's first goal, directing a bullet header past Guglielmo Vicario from an Everton corner.
Beto, in the meantime, missed a number of opportunities, while the Italian goalkeeper made a series of excellent stops to ensure Tottenham went five away games without defeat in the Premier League.
But the VAR stepped in, instructing the match official to review the score on the pitchside monitor and the official decided that the winger and Iliman Ndiaye were in an illegal position and had interfered with the Spurs keeper.
This victory moves Thomas Frank's team into third place in the Premier League, five points off local foes and table-toppers Arsenal.
Everton remain in 14th position and sit half a dozen points clear of the drop zone.
Tottenham analysis: Van de Ven excels in duties at both ends of the field
After a drab midweek performance in the Champions League against the French side, where they managed a mere attempts on goal, the manager chose Randal Kolo Muani up front instead of ex-Everton forward the Brazilian.
The new arrival was failed to influence the game before being replaced for the substitute after an hour on the pitch, but it emerged he proved unnecessary in the end.
Defender the Dutchman converted into an offensive threat to be reckoned with.
Tottenham's opening strike came from a well-worked set-piece play, with the midfielder heading the ball back across the face of goal for an free Van de Ven to head home.
And Ven de Ven - stepping up as skipper in Cristian Romero's absence - notched his second in first-half stoppage time as he rose above Jordan Pickford to head home.
The Dutchman was just as impressive in defence, combining effectively with his defensive colleague as the duo dealt excellently with the 34 crosses sent their way by Everton.
Toffees breakdown: Everton missing finishing touch
Everton's recent stadium had been a fortress, but it seems the novelty may have worn off slightly and fans flocked to the exits after Sarr's third for Tottenham.
The break in the team's winning streak at home will not be a massive concern for the manager, but their striker situation will be.
Beto and Thierno Barry - the Everton's two recognised centre-forwards - had netted just one league goal combined before Sunday's outing.
And they were unable to contribute to that miserable record on a wet and gloomy evening on in Liverpool.
Beto's performance was epitomized when he chose to bicycle-kick a clear chance from close range, despite having room and opportunity to readjust for a more conventional attempt that would have challenged Vicario.
Barry, too, failed to make an impact after replacing the starter in the second half.
It wasn't for a shortage of chance. The majority of Everton's offensive moves came through the winger and the forward, who relentlessly delivered dangerous balls into the Spurs penalty area.
What next for these two sides?
Everton: The team travel to the Stadium of Light in the Premier League on early November at 20:00 GMT.
Spurs: The London club travel to St James' Park on Wednesday, 29 October for their next round Carabao Cup match against Newcastle.