Micky van de Ven became the initial defender to net two goals in a Premier League match for Spurs since the Belgian defender in spring 2013.
Key points
Micky Van de Ven heads into the net two times in opening period
The home side's Jake O'Brien has goal disallowed after video check
Senegalese midfielder scores third in dying moments
The defeat is Everton's initial at their new ground
Micky van de Ven found the net on two occasions as Tottenham prolonged their winning streak in away games in the top division and handed the Toffees their initial loss at Hill Dickinson Stadium.
Everton were undefeated in their five previous fixtures 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 Van de Ven pounced twice from corners in the opening 45 minutes to place their impressive record at jeopardy, and they were failed to mount a comeback before the midfielder - set up by ex-Everton forward the Brazilian - headed home a third to seal the victory.
Jake O'Brien thought he had levelled the tally five minutes after Van de Ven's first goal, directing a powerful header past Guglielmo Vicario from an set-piece.
The Portuguese striker, in the meantime, missed a handful of chances, while Vicario made a series of excellent saves to ensure Tottenham went five matches on the road without defeat in the Premier League.
But the VAR intervened, advising the match official to check the score on the screen and the referee ruled that Jack Grealish and the attacker were in an illegal position and had interfered with the Tottenham goalkeeper.
This victory moves the manager's side into third place in the division, a handful of points off local foes and leaders Arsenal.
The Merseyside club stay 14th and are six points ahead of the drop zone.
After a drab weekday performance in the European competition against Monaco, where they mustered a only attempts on goal, Frank opted for the French striker up front instead of former Toffees player the Brazilian.
The summer signing was unable to make much of an impact before being substituted for the substitute after an hour on the field, but it emerged he wasn't needed in the final outcome.
Defender the Dutchman transformed into an offensive threat to be feared.
Spurs' opening strike came from a well-worked corner routine, with the midfielder heading the ball back across the face of goal for an free Van de Ven to score.
And Ven de Ven - filling in as skipper in Cristian Romero's absence - added his next goal in added time as he outjumped the England keeper to nod in.
Van de Ven was just as outstanding in defensive duties, combining well with his defensive colleague as the duo handled superbly with the numerous deliveries sent their way by Everton.
The club's recent stadium had been a fortress, but it appears the freshness may have faded somewhat and supporters flocked to the exits after Sarr's third for Spurs.
The break in Everton's unbeaten home run won't be a massive concern for David Moyes, but their striker situation will be.
The forward and Thierno Barry - the Toffees' two established centre-forwards - had scored only a single goal between them before the weekend's outing.
And they were unable to contribute to that poor tally on a wet and gloomy evening on Merseyside.
The striker's performance was epitomized when he opted to overhead kick a clear chance from close range, even with having space and time to reposition for a more conventional attempt that would have tested Vicario.
The substitute, as well, was unable to influence the game after coming on for Beto in the second half.
It was not for a lack of opportunity. Most of Everton's attacks came through the winger and Ndiaye, who tirelessly whipped dangerous balls into the Tottenham penalty area.
Everton: Moyes' men head to the Stadium of Light in the Premier League on early November at 8 PM.
Spurs: The London club travel to St James' Park on Wednesday, 29 October for their next round League Cup match against the Magpies.
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