Micky van de Ven emerged as the initial backline player to net two goals in a Premier League game for Tottenham since Jan Vertonghen in March 2013.
Key points
The Spurs defender nods home twice in opening period
Everton's Jake O'Brien has equalizer disallowed after video check
Senegalese midfielder nets third in dying moments
This loss is the Merseyside club's first at Hill Dickinson Stadium
Micky van de Ven scored on two occasions as Tottenham prolonged their winning streak in away games in the top division and handed Everton their initial loss at their new home.
The Toffees were unbeaten in their last five matches at their recently opened stadium at the dockside location, having left their historic home behind after more than a century at the conclusion of last season.
But Tottenham's leader the Dutchman struck twice from corners in the opening 45 minutes to place their impressive record at risk, and they were unable to mount a comeback before Pape Matar Sarr - set up by ex-Everton forward Richarlison - headed home a final goal to seal the victory.
Jake O'Brien believed he had equalized the scores a short while after the defender's first goal, glancing 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 succession of excellent stops to guarantee the London club went five away games unbeaten in the Premier League.
But the VAR intervened, instructing Craig Pawson to review the score on the screen and the referee decided that the winger and Iliman Ndiaye were in an illegal position and had interfered with the Tottenham goalkeeper.
The win elevates Thomas Frank's team up to third in the Premier League, a handful of points off north London rivals and table-toppers the Gunners.
The Merseyside club remain in 14th position and are half a dozen points clear of the relegation zone.
Following a drab midweek display in the Champions League against Monaco, where they managed a mere two shots on target, Frank chose the French striker in attack instead of ex-Everton forward Richarlison.
The new arrival was unable to influence the game before being replaced for Richarlison after 60 minutes on the pitch, but it turns out he proved unnecessary in the end.
Centre-back the Dutchman transformed into an offensive threat to be reckoned with.
Tottenham's opening strike came from a cleverly executed corner routine, with the midfielder directing the ball back across the face of goal for an unmarked Van de Ven to head home.
And the captain - stepping up as skipper in the Argentine's unavailability - added his next goal in first-half stoppage time as he rose above Jordan Pickford to head home.
The Dutchman was just as impressive in defensive duties, partnering well with Kevin Danso as the pair handled superbly with the 34 crosses thrown their way by the opposition.
The club's new home had been a happy hunting ground, but it appears the novelty may have worn off somewhat and supporters headed to the gates after Sarr's final goal for Spurs.
The end in the team's winning streak at home won't be a massive worry for David Moyes, but their attacking woes will be.
Beto and the other striker - the Everton's two established centre-forwards - had netted just one league goal between them before the weekend's outing.
And they were failed to add to that poor tally on a damp and dreary night on in Liverpool.
The striker's performance was epitomized when he chose to overhead kick a golden opportunity from near the goal, even with having room and opportunity to reposition for a simpler attempt that would have challenged Vicario.
Barry, too, was unable to make an impact after coming on for the starter in the 65th minute.
It wasn't for a lack of opportunity. Most of the home side's offensive moves came through Grealish and Ndiaye, who relentlessly delivered dangerous crosses into the Spurs penalty area.
Everton: The team travel to Sunderland in the Premier League on Monday, 3 November at 20:00 GMT.
Tottenham: The London club travel to St James' Park on Wednesday, 29 October for their next round League Cup tie against the Magpies.
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