Micky van de Ven became the initial backline player to score twice in a English top-flight game for Tottenham since Jan Vertonghen in spring 2013.
At a glance
The Spurs defender heads into the net twice in first half
Everton's Jake O'Brien has equalizer disallowed after video check
Pape Matar Sarr nets final goal in 89th minute
This loss is Everton's initial at Hill Dickinson Stadium
The Tottenham defender found the net twice as Tottenham extended their winning streak in away games in the top division and delivered the Toffees their initial loss at Hill Dickinson Stadium.
Everton were undefeated in their last five matches at their new ground at the dockside location, having departed Goodison Park behind after more than a century at the conclusion of the previous campaign.
But Tottenham's leader Van de Ven struck twice from set-pieces in the first half to place their strong form at jeopardy, and they were failed to turn it around before Pape Matar Sarr - assisted by former Toffees attacker Richarlison - headed home a third to seal the victory.
The Everton defender thought he had levelled the tally five minutes after Van de Ven's opener, directing a bullet header past Guglielmo Vicario from an Everton corner.
Beto, in the meantime, failed to convert a handful of opportunities, while the Italian goalkeeper made a series of excellent saves to ensure Tottenham went five matches on the road unbeaten in the Premier League.
But the video assistant referee intervened, instructing Craig Pawson to review the goal on the screen and the referee decided that the winger and the attacker were in offside positions and had interfered with the Tottenham goalkeeper.
This victory elevates Thomas Frank's team up to third in the division, five points off north London rivals and table-toppers the Gunners.
The Merseyside club stay in 14th position and are six points ahead of the drop zone.
Following a uninspiring midweek display in the European competition against the French side, where they mustered a mere attempts on target, Frank chose the French striker up front instead of former Toffees player the Brazilian.
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 wasn't needed in the final outcome.
Defender Van de Ven converted into an attacking force to be reckoned with.
Spurs' opening strike came from a well-worked set-piece play, with Rodrigo Bentancur directing the ball back across the face of goal for an unmarked the defender to score.
And the captain - stepping up as captain in the Argentine's unavailability - notched his second in first-half stoppage time as he rose above the England keeper to nod in.
Van de Ven was just as outstanding in defensive duties, combining well with Kevin Danso as the pair handled superbly with the numerous deliveries thrown their way by the opposition.
The club's new home had been a happy hunting ground, but it appears the freshness may have worn off somewhat and supporters headed to the gates after the midfielder's final goal for Tottenham.
The end in Everton's winning streak at home won't be a major concern for David Moyes, but their striker situation will be.
Beto and Thierno Barry - the Toffees' two recognised centre-forwards - had scored only one league goal between them before the weekend's match.
And they were unable to add to that miserable tally on a wet and gloomy night on Merseyside.
The striker's form was summed up when he chose to bicycle-kick a clear chance from near the goal, despite having room and opportunity to reposition for a simpler shot that would have tested Vicario.
Barry, as well, was unable to make an impact after replacing Beto in the second half.
It was not for a lack of chance. The majority of the home side's attacks came through the winger and the forward, who tirelessly whipped threatening balls into the Spurs penalty area.
Everton: Moyes' men travel to Sunderland in the top flight on Monday, 3 November at 20:00 GMT.
Spurs: The London club travel to St James' Park on late October for their next round Carabao Cup tie against the Magpies.
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