Micky van de Ven became the first backline player to score twice in a English top-flight match for Spurs since Jan Vertonghen in spring 2013.
Match summary
The Spurs defender nods into the net two times in opening period
Everton's Jake O'Brien has goal ruled after VAR review
Pape Matar Sarr nets third in 89th minute
The defeat is the Merseyside club's initial at Hill Dickinson Stadium
Micky van de Ven scored twice as Tottenham prolonged their unbeaten run in away games in the Premier League and handed Everton their first defeat at Hill Dickinson Stadium.
Everton were undefeated in their five previous fixtures at their new ground at Bramley-Moore Dock, having departed Goodison Park behind after 133 years at the end of last season.
But Spurs captain Van de Ven pounced twice from set-pieces in the first half to place their strong form at risk, and they were failed to turn it around before the midfielder - assisted by ex-Everton forward the Brazilian - nodded in a final goal to put the game to bed.
Jake O'Brien believed he had levelled the tally a short while after Van de Ven's opener, directing a powerful header past the Spurs keeper from an Everton corner.
Beto, in the meantime, missed a handful of chances, while the Italian goalkeeper made a succession of fine stops to guarantee the London club went five away games unbeaten in the English top flight.
But the video assistant referee stepped in, instructing Craig Pawson to review the goal on the screen and the official ruled that Jack Grealish and Iliman Ndiaye were in an illegal position and had interfered with the Tottenham goalkeeper.
The win elevates the manager's team up to third in the division, five points off local foes and leaders Arsenal.
Everton stay in 14th position and sit six points ahead of the relegation zone.
After a uninspiring midweek display in the Champions League against Monaco, where they managed a only attempts on goal, the manager chose the French striker up front instead of former Toffees player the Brazilian.
The summer signing was unable to make much of an impact before being replaced for Richarlison after an hour on the field, but it emerged he wasn't needed in the end.
Centre-back the Dutchman converted into an offensive threat to be reckoned with.
Spurs' opening strike came from a cleverly executed set-piece play, with Rodrigo Bentancur directing the ball back across the face of goal for an free the defender to head home.
And Ven de Ven - filling in as skipper in the Argentine's absence - notched his second in added time as he outjumped the England keeper to head home.
The Dutchman was equally outstanding in defence, combining effectively with Kevin Danso as the pair dealt superbly with the 34 crosses thrown their way by Everton.
Everton's recent stadium had been a happy hunting ground, but it appears the novelty may have worn off somewhat and fans flocked to the gates after Sarr's third for Spurs.
The break in the team's winning streak at home won't be a massive concern for the manager, but their attacking woes are.
Beto and Thierno Barry - the Everton's pair of recognised centre-forwards - had scored just a single goal between them before the weekend's match.
And they were failed to add to that miserable tally on a wet and gloomy evening on in Liverpool.
Beto's performance was summed up when he opted to overhead kick a golden opportunity from near the goal, even with having room and time to reposition for a simpler shot that would have challenged Vicario.
Barry, as well, was unable to make an impact after coming on for the starter in the 65th minute.
It was not for a shortage of chance. The majority of the home side's offensive moves came through Grealish and the forward, who tirelessly delivered dangerous crosses into the Tottenham box.
The Toffees: The team travel to Sunderland in the Premier League on early November at 8 PM.
Tottenham: The London club go to St James' Park on late October for their fourth-round Carabao Cup match against Newcastle.
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