Micky van de Ven emerged as the first backline player to score two goals in a Premier League game for Spurs since the Belgian defender in spring 2013.
Match summary
The Spurs defender heads home twice in opening period
Everton's Jake O'Brien has equalizer ruled after VAR review
Senegalese midfielder nets final goal in 89th minute
This loss is the Merseyside club's initial at their new ground
Micky van de Ven scored twice as Tottenham extended their winning streak in away games in the Premier League and delivered Everton their first defeat at their new home.
The Toffees were unbeaten in their five previous fixtures at their recently opened stadium at Bramley-Moore Dock, having left Goodison Park behind after 133 years at the end of the previous campaign.
But Spurs captain Van de Ven pounced 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 Pape Matar Sarr - set up by former Toffees attacker Richarlison - nodded in a final goal to seal the victory.
Jake O'Brien believed he had equalized the tally five minutes after the defender's first goal, glancing a powerful header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, in the meantime, failed to convert a handful of chances, while Vicario made a succession of fine saves to ensure the London club went five matches on the road unbeaten in the English top flight.
But the video assistant referee intervened, instructing Craig Pawson to review the score on the pitchside monitor and the referee decided that the winger and Iliman Ndiaye were in an illegal position and had impeded with the Tottenham goalkeeper.
This victory moves the manager's team up to third in the division, a handful of points off local foes and table-toppers the Gunners.
The Merseyside club stay in 14th position and sit half a dozen points clear of the relegation zone.
Following a uninspiring midweek display in the European competition against Monaco, where they mustered a only two shots on target, the manager opted for Randal Kolo Muani up front instead of ex-Everton forward Richarlison.
The summer signing was unable to make much of an impact before being substituted for Richarlison after 60 minutes on the pitch, but it turns out he proved unnecessary in the final outcome.
Centre-back Van de Ven transformed into an attacking force to be reckoned with.
Tottenham's opening strike came from a cleverly executed corner routine, with Rodrigo Bentancur directing the ball back across the face of goal for an free Van de Ven to head home.
And the captain - filling in as skipper in Cristian Romero's absence - added his second in added time as he outjumped the England keeper to nod in.
Van de Ven was equally impressive in defensive duties, partnering effectively with his defensive colleague as the pair handled excellently with the 34 crosses thrown their way by Everton.
The club's new home had been a happy hunting ground, but it appears the novelty may have worn off somewhat and fans flocked to the gates after the midfielder's third for Spurs.
The break in Everton's unbeaten home run will not be a major concern for the manager, but their striker situation are.
The forward and the other striker - the Everton's pair of recognised strikers - had netted just a single goal between them before the weekend's match.
And they were failed to contribute to that poor record on a wet and gloomy evening on in Liverpool.
Beto's form was summed up when he chose to overhead kick a clear chance from near the goal, even with having space and opportunity to reposition for a simpler shot that would have challenged Vicario.
The substitute, too, was unable to make an impact after replacing Beto in the 65th minute.
It was not for a lack of chance. The majority of Everton's offensive moves came through Grealish and the forward, who relentlessly whipped threatening crosses into the Spurs box.
The Toffees: The team travel to Sunderland in the top flight on Monday, 3 November at 20:00 GMT.
Tottenham: The London club travel to St James' Park on Wednesday, 29 October for their fourth-round League Cup tie against the Magpies.
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Brian Hernandez
Brian Hernandez