Micky van de Ven Double Ends The Toffees' Run at Brand New Home Ground
The Dutch defender became the first backline player to score twice in a Premier League match for Spurs since Jan Vertonghen in March 2013.
At a glance
Micky Van de Ven nods into the net twice in opening period
The home side's Jake O'Brien has equalizer disallowed after video check
Senegalese midfielder scores third in dying moments
This loss is Everton's initial at their new ground
Micky van de Ven scored on two occasions as Spurs extended their winning streak on the road in the top division and handed the Toffees their initial loss at Hill Dickinson Stadium.
Everton were unbeaten in their five previous fixtures at their recently opened stadium at the dockside location, having left their historic home behind after more than a century at the end of last season.
But Tottenham's leader Van de Ven 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 former Toffees attacker the Brazilian - nodded in a final goal to put the game to bed.
Jake O'Brien believed he had equalized the tally a short while after Van de Ven's opener, directing a powerful header past Guglielmo Vicario from an set-piece.
Beto, meanwhile, failed to convert a handful of opportunities, while the Italian goalkeeper made a series of excellent saves to ensure the London club went five matches on the road unbeaten in the English top flight.
But the VAR stepped in, advising Craig Pawson to check the goal on the screen and the referee decided that the winger and the attacker were in offside positions and had impeded with the Spurs keeper.
This victory elevates Thomas Frank's side into third place in the Premier League, a handful of points off local foes and table-toppers Arsenal.
Everton remain in 14th position and sit six points clear of the relegation zone.
Tottenham analysis: The defender fulfils duties at both ends of pitch
Following a uninspiring midweek display in the Champions League against Monaco, where they mustered a only attempts on target, Frank opted for Randal Kolo Muani in attack instead of former Toffees player Richarlison.
The new arrival was failed to influence the game before being replaced for the substitute after an hour on the pitch, but it turns out he wasn't needed in the end.
Defender Van de Ven transformed into an offensive threat to be reckoned with.
Tottenham's opening strike came from a well-worked corner routine, with the midfielder directing the ball back across the six-yard box for an free Van de Ven to score.
And Ven de Ven - filling in as skipper in Cristian Romero's absence - notched his next goal in first-half stoppage time as he outjumped the England keeper to head home.
Van de Ven was just as outstanding in defence, combining effectively with Kevin Danso as the duo dealt excellently with the 34 crosses sent their way by the opposition.
Toffees breakdown: Toffees missing striker's instinct
Everton's new home had been a happy hunting ground, but it seems the novelty may have faded somewhat and fans flocked to the exits after Sarr's third for Tottenham.
The break in the team's unbeaten home run will not be a major concern for David Moyes, but their attacking woes are.
The forward and the other striker - the Toffees' pair of established strikers - had scored only a single goal between them before the weekend's match.
And they were failed to add to that miserable tally on a damp and dreary night on Merseyside.
Beto's performance was epitomized when he opted to overhead kick a clear chance from near the goal, even with having room and time to reposition for a more conventional attempt that would have tested the keeper.
Barry, as well, failed to make an impact after coming on for the starter in the 65th minute.
It was not for a lack of opportunity. The majority of Everton's attacks came through Grealish and Ndiaye, who relentlessly delivered dangerous balls into the Spurs penalty area.
Upcoming fixtures for these two sides?
The Toffees: The team travel to the Stadium of Light in the Premier League on Monday, 3 November at 20:00 GMT.
Tottenham: Spurs go to St James' Park on Wednesday, 29 October for their next round League Cup tie against the Magpies.