Micky van de Ven emerged as the initial defender to score twice in a English top-flight match for Tottenham since the Belgian defender in spring 2013.
Match summary
Micky Van de Ven heads into the net two times in first half
The home side's Jake O'Brien has goal disallowed after video check
Senegalese midfielder scores third in 89th minute
The defeat is the Merseyside club's initial at their new ground
The Tottenham defender found the net twice as Spurs prolonged their unbeaten run in away games in the Premier League and handed the Toffees their first defeat at their new home.
The Toffees were undefeated in their last five matches at their new ground at Bramley-Moore Dock, having left Goodison Park behind after more than a century at the end of last season.
But Spurs captain the Dutchman pounced twice from set-pieces in the first half to place their strong form at jeopardy, and they were unable to turn it around before Pape Matar Sarr - assisted by former Toffees attacker the Brazilian - headed home a final goal to put the game to bed.
Jake O'Brien thought he had equalized the tally five minutes after Van de Ven's first goal, directing a bullet header past Guglielmo Vicario from an set-piece.
The Portuguese striker, meanwhile, missed a number of chances, while the Italian goalkeeper made a series of excellent saves to ensure the London club went five matches on the road without defeat in the English top flight.
But the video assistant referee stepped in, advising the match official to review the goal on the pitchside monitor and the official decided that the winger and the attacker were in an illegal position and had interfered with the Tottenham goalkeeper.
This victory elevates the manager's side into third place in the Premier League, a handful of points off local foes and table-toppers Arsenal.
Everton stay in 14th position and sit half a dozen points clear of the relegation zone.
After a uninspiring midweek performance in the Champions League against the French side, where they managed a only attempts on goal, the manager opted for Randal Kolo Muani in attack instead of ex-Everton forward the Brazilian.
The summer signing was unable to make much of an impact before being replaced for the substitute after 60 minutes on the pitch, but it turns out he proved unnecessary in the final outcome.
Centre-back Van de Ven transformed into an offensive threat to be reckoned with.
Spurs' opening strike came from a well-worked set-piece play, with the midfielder heading the ball back across the face of goal for an unmarked the defender to score.
And Ven de Ven - stepping up as captain in the Argentine's absence - notched his next goal in first-half stoppage time as he outjumped Jordan Pickford to head home.
Van de Ven was just as outstanding in defensive duties, partnering well with his defensive colleague as the duo handled superbly with the numerous deliveries sent their way by the opposition.
Everton's recent stadium had been a fortress, but it seems the novelty may have worn off somewhat and fans flocked to the exits after Sarr's final goal for Spurs.
The break in the team's unbeaten home run won't be a massive worry for the manager, but their attacking woes are.
Beto and the other striker - the Everton's pair of recognised centre-forwards - had scored only a single goal combined before the weekend's outing.
And they were unable to contribute to that poor record on a wet and gloomy night on in Liverpool.
The striker's form was epitomized when he opted to bicycle-kick a clear chance from close range, even with having room and time to readjust for a more conventional attempt that would have tested the keeper.
Barry, as well, was unable to make an impact after coming on for Beto in the 65th minute.
It was not for a shortage of chance. The majority of the home side's offensive moves came through the winger and Ndiaye, who relentlessly whipped threatening crosses into the Spurs penalty area.
Everton: The team travel to the Stadium of Light in the top flight on Monday, 3 November at 20:00 GMT.
Spurs: The London club go to St James' Park on Wednesday, 29 October for their fourth-round Carabao Cup tie against Newcastle.
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