Micky van de Ven Double Ends Everton's Run at New Stadium
Micky van de Ven emerged as the first backline player to score two goals in a English top-flight match for Spurs since the Belgian defender in March 2013.
Match summary
The Spurs defender heads into the net twice in first half
Everton's Jake O'Brien has equalizer ruled after VAR review
Senegalese midfielder scores third in 89th minute
The defeat is the Merseyside club's first at their new ground
Micky van de Ven found the net on two occasions as Spurs prolonged their unbeaten run in away games in the Premier League and handed Everton their first defeat at their new home.
The Toffees were undefeated in their last five matches at their recently opened stadium at Bramley-Moore Dock, having left their historic home behind after more than a century at the end of the previous campaign.
But Tottenham's leader the Dutchman struck twice from set-pieces in the opening 45 minutes to put their strong form at jeopardy, and they were failed to mount a comeback before the midfielder - assisted by ex-Everton forward the Brazilian - nodded in a third to seal the victory.
The Everton defender believed he had equalized the scores a short while after the defender's opener, directing a bullet header past Guglielmo Vicario from an set-piece.
Beto, in the meantime, missed a handful of opportunities, while Vicario made a succession of excellent stops to ensure the London club went five away games unbeaten in the Premier League.
But the video assistant referee stepped in, instructing the match official to check the score on the pitchside monitor and the referee decided that Jack Grealish and the attacker were in offside positions and had impeded with the Spurs keeper.
This victory elevates Thomas Frank's side up to third in the division, a handful of points off north London rivals and table-toppers Arsenal.
Everton remain in 14th position and sit six points ahead of the drop zone.
Spurs breakdown: Van de Ven fulfils duties at both ends of the field
Following a drab weekday performance in the Champions League against Monaco, where they managed a mere two shots on target, the manager chose Randal Kolo Muani in attack instead of ex-Everton forward Richarlison.
The new arrival was failed to influence the game before being substituted for the substitute after 60 minutes on the pitch, but it emerged he proved unnecessary in the end.
Centre-back the Dutchman converted into an attacking force to be feared.
Tottenham's first goal came from a well-worked corner routine, with Rodrigo Bentancur directing the ball toward the face of goal for an free the defender to head home.
And Ven de Ven - filling in as captain in the Argentine's unavailability - added his second in first-half stoppage time as he outjumped Jordan Pickford to nod in.
The Dutchman was just as outstanding in defensive duties, partnering effectively with his defensive colleague as the duo dealt superbly with the numerous deliveries thrown their way by the opposition.
Everton analysis: Toffees missing striker's instinct
Everton's recent stadium had been a happy hunting ground, but it seems the novelty may have faded slightly and supporters flocked to the gates after Sarr's final goal for Tottenham.
The break in Everton's unbeaten home run won't be a massive worry for the manager, but their attacking woes are.
The forward and Thierno Barry - the Everton's pair of recognised strikers - had netted only one league goal combined before the weekend's outing.
And they were failed to contribute to that miserable tally on a damp and dreary evening on in Liverpool.
The striker's performance was epitomized when he chose to overhead kick a golden opportunity from close range, despite having room and time to readjust for a more conventional attempt that would have tested the keeper.
Barry, too, was unable to make an impact after replacing the starter in the second half.
It wasn't for a lack of opportunity. The majority of Everton's offensive moves came through the winger and the forward, who relentlessly whipped threatening balls into the Tottenham penalty area.
What next for both teams?
Everton: Moyes' men travel to Sunderland in the top flight on Monday, 3 November at 20:00 GMT.
Tottenham: Spurs go to St James' Park on Wednesday, 29 October for their fourth-round League Cup tie against the Magpies.