Micky van de Ven emerged as the initial backline player to net two goals in a English top-flight match for Spurs since the Belgian defender in March 2013.
Match summary
Micky Van de Ven nods into the net two times in opening period
Everton's Jake O'Brien has equalizer disallowed after video check
Senegalese midfielder scores third in dying moments
This loss is Everton's first at their new ground
Micky van de Ven scored on two occasions as Tottenham extended their winning streak on the road in the top division and handed Everton their initial loss at their new home.
Everton were unbeaten in their last five matches 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 twice from corners in the opening 45 minutes to put their impressive record at risk, and they were unable to turn it around before Pape Matar Sarr - assisted by ex-Everton forward the Brazilian - nodded in a third to seal the victory.
Jake O'Brien thought he had equalized the tally a short while after the defender's first goal, glancing a bullet header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, meanwhile, missed a handful of opportunities, while the Italian goalkeeper made a succession of fine stops to guarantee the London club went five matches on the road without defeat in the Premier League.
But the VAR stepped in, advising the match official to check the goal on the pitchside monitor and the referee decided that Jack Grealish and the attacker were in offside positions and had interfered with the Spurs keeper.
The win moves the manager's side into third place in the division, five points off north London rivals and leaders Arsenal.
Everton remain 14th and are six points ahead of the drop zone.
After a drab weekday display in the Champions League against Monaco, where they managed a only two shots on goal, the manager opted for Randal Kolo Muani in attack instead of former Toffees player Richarlison.
The new arrival was unable to make much of an impact before being replaced for the substitute after an hour on the pitch, but it emerged he proved unnecessary in the final outcome.
Centre-back Van de Ven converted into an offensive threat to be feared.
Spurs' first goal came from a cleverly executed corner routine, with the midfielder heading the ball toward the six-yard box for an unmarked the defender to score.
And Ven de Ven - filling in as captain in the Argentine's unavailability - added his next goal in added time as he rose above the England keeper to nod in.
The Dutchman was just as impressive in defence, combining well with Kevin Danso as the duo dealt excellently with the 34 crosses sent their way by the opposition.
Everton's recent stadium had been a happy hunting ground, but it seems the freshness may have worn off slightly and fans flocked to the exits after the midfielder's final goal for Tottenham.
The end in Everton's unbeaten home run won't be a major worry for David Moyes, but their striker situation will be.
The forward and Thierno Barry - the Toffees' pair of established centre-forwards - had netted only one league goal combined before the weekend's match.
And they were unable to contribute to that miserable record on a damp and dreary night on in Liverpool.
Beto's form was summed up when he opted to bicycle-kick a golden opportunity from close range, even with having room and opportunity to reposition for a simpler attempt that would have tested the keeper.
The substitute, too, failed to make an impact after replacing Beto in the 65th minute.
It was not for a lack of opportunity. The majority of the home side's offensive moves came through the winger and the forward, who relentlessly whipped threatening balls into the Spurs penalty area.
Everton: The team travel to the Stadium of Light in the top flight on early November at 8 PM.
Tottenham: The London club go to Newcastle's ground on late October for their fourth-round League Cup match against the Magpies.
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