Micky van de Ven became the first defender to net twice in a Premier League game for Spurs since Jan Vertonghen in March 2013.
At a glance
The Spurs defender heads into the net two times in first half
The home side's defender has equalizer ruled after video check
Senegalese midfielder scores third in dying moments
This loss is Everton's first at their new ground
The Tottenham defender found the net twice as Tottenham extended their winning streak on the road in the top division and handed the Toffees their initial loss 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 Spurs captain Van de Ven struck twice from set-pieces in the first half to place their impressive record at risk, and they were failed to turn it around before the midfielder - set up by former Toffees attacker the Brazilian - nodded in a third to seal the victory.
Jake O'Brien believed he had equalized the tally five minutes after the defender's opener, glancing a bullet header past Guglielmo Vicario from an Everton corner.
Beto, meanwhile, missed a number of opportunities, while the Italian goalkeeper made a series of fine stops to guarantee Tottenham went five away games unbeaten in the Premier League.
But the video assistant referee intervened, advising Craig Pawson to review the score on the screen and the official ruled that the winger and the attacker were in an illegal position and had interfered with the Tottenham goalkeeper.
This victory elevates the manager's team up to third in the division, five points off local foes and leaders the Gunners.
The Merseyside club stay in 14th position and are six points clear of the drop zone.
After a drab weekday display in the Champions League against Monaco, where they managed a only attempts on target, the manager opted for Randal Kolo Muani in attack instead of former Toffees player the Brazilian.
The new arrival was unable to influence the game before being substituted for the substitute after 60 minutes on the pitch, but it emerged he proved unnecessary in the final outcome.
Centre-back Van de Ven transformed into an attacking force to be feared.
Spurs' first goal came from a cleverly executed corner routine, with Rodrigo Bentancur directing the ball toward the face of goal for an unmarked the defender to score.
And Ven de Ven - filling in as skipper in the Argentine's unavailability - notched his next goal in added time as he rose above Jordan Pickford to nod in.
The Dutchman was just as outstanding in defence, partnering well with his defensive colleague as the pair dealt excellently with the 34 crosses thrown their way by the opposition.
The club's new home had been a happy hunting ground, but it seems the novelty may have faded somewhat and supporters flocked to the exits after Sarr's third for Tottenham.
The end in Everton's unbeaten home run won't be a massive worry for David Moyes, but their attacking woes will be.
The forward and Thierno Barry - the Everton's two established strikers - had scored only a single goal between them before the weekend's outing.
And they were failed to add to that poor tally on a damp and dreary night on in Liverpool.
The striker's form was summed up when he chose to bicycle-kick a clear chance from near the goal, even with having room and opportunity to readjust for a simpler shot that would have challenged Vicario.
Barry, as well, was unable to make an impact after replacing the starter in the second half.
It wasn't for a shortage of opportunity. The majority of Everton's offensive moves came through the winger and Ndiaye, who tirelessly whipped dangerous crosses into the Spurs penalty area.
The Toffees: Moyes' men head to Sunderland in the top flight on early November at 20:00 GMT.
Spurs: The London club go to St James' Park on Wednesday, 29 October for their fourth-round League Cup tie against Newcastle.
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