Micky van de Ven became the initial defender to score twice in a English top-flight match for Tottenham since the Belgian defender in March 2013.
Key points
The Spurs defender nods home twice in opening period
Everton's Jake O'Brien has equalizer ruled after VAR review
Pape Matar Sarr scores third in dying moments
The defeat is Everton's first at their new ground
The Tottenham defender found the net on two occasions as Tottenham extended their winning streak in away games in the top division and delivered Everton their initial loss at their new home.
Everton were unbeaten in their five previous fixtures at their new ground at Bramley-Moore Dock, having departed Goodison Park behind after 133 years at the conclusion of last season.
But Tottenham's leader the Dutchman struck on two occasions from corners in the opening 45 minutes to place their impressive record at jeopardy, and they were failed to mount a comeback before Pape Matar Sarr - set up by ex-Everton forward Richarlison - nodded in 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 powerful header past the Spurs keeper from an set-piece.
Beto, meanwhile, failed to convert a number of chances, while the Italian goalkeeper made a succession of excellent stops to guarantee Tottenham went five matches on the road without defeat in the Premier League.
But the VAR stepped in, instructing the match official to review the score on the screen and the referee ruled that Jack Grealish and the attacker were in offside positions and had impeded with the Tottenham goalkeeper.
This victory moves Thomas Frank's team into third place in the Premier League, five points off north London rivals and table-toppers Arsenal.
Everton remain in 14th position and are half a dozen points ahead of the relegation zone.
Following a uninspiring midweek display in the Champions League against the French side, where they managed a only two shots on target, Frank opted for the French striker up front instead of ex-Everton forward Richarlison.
The summer signing was unable to influence the game before being substituted for Richarlison after an hour on the field, but it turns out he proved unnecessary in the end.
Defender Van de Ven converted into an offensive threat to be feared.
Tottenham's opening strike came from a cleverly executed corner routine, with the midfielder directing the ball back across the six-yard box for an free Van de Ven to head home.
And Ven de Ven - stepping up as skipper in the Argentine's absence - added his second in added time as he rose above Jordan Pickford to nod in.
Van de Ven was equally impressive in defensive duties, partnering well with his defensive colleague as the duo handled excellently with the 34 crosses sent their way by Everton.
The club's recent stadium had been a happy hunting ground, but it seems the novelty may have faded slightly and fans headed to the gates after Sarr's third for Spurs.
The end in Everton's winning streak at home won't be a massive concern for David Moyes, but their attacking woes are.
Beto and the other striker - the Everton's two recognised centre-forwards - had netted just a single goal combined before the weekend's match.
And they were unable to contribute to that poor record on a damp and dreary night on Merseyside.
The striker's form was epitomized when he opted to overhead kick a clear chance from close range, despite having room and opportunity to readjust for a simpler attempt that would have tested the keeper.
Barry, as well, was unable to make an impact after coming on for the starter in the 65th minute.
It was not for a lack of chance. Most of the home side's attacks came through the winger and the forward, who relentlessly delivered threatening crosses into the Spurs box.
Everton: The team head to Sunderland in the Premier League on early November at 8 PM.
Tottenham: Spurs go to St James' Park on Wednesday, 29 October for their fourth-round League Cup match against the Magpies.
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