Micky van de Ven emerged as the first defender to score two goals in a Premier League match for Spurs since Jan Vertonghen in March 2013.
At a glance
Micky Van de Ven nods into the net two times in opening period
The home side's Jake O'Brien has goal disallowed after VAR review
Senegalese midfielder scores final goal in dying moments
The defeat is the Merseyside club's initial at Hill Dickinson Stadium
The Tottenham defender scored on two occasions as Spurs prolonged their winning streak on the road in the Premier League and handed Everton their first defeat at their new home.
Everton were unbeaten in their five previous fixtures at their recently opened stadium at the dockside location, having departed Goodison Park behind after more than a century at the end of the previous campaign.
But Tottenham's leader the Dutchman pounced twice from corners in the first half to put their impressive record at risk, and they were failed to mount a comeback before Pape Matar Sarr - assisted by former Toffees attacker the Brazilian - nodded in a final goal to put the game to bed.
The Everton defender 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.
Beto, meanwhile, missed a handful of opportunities, while the Italian goalkeeper made a series of excellent stops to ensure the London club went five away games unbeaten in the Premier League.
But the video assistant referee stepped in, instructing the match official to check the goal on the screen and the official decided that Jack Grealish and the attacker were in offside positions and had impeded with the Tottenham goalkeeper.
This victory elevates the manager's team into third place in the Premier League, a handful of points off north London rivals and leaders Arsenal.
The Merseyside club remain in 14th position and sit half a dozen points clear of the drop zone.
After a drab midweek display in the Champions League against the French side, where they managed a mere two shots on goal, the manager opted for the French striker in attack instead of former Toffees player Richarlison.
The summer signing was unable to influence the game before being replaced for Richarlison after an hour on the field, but it emerged he wasn't needed in the end.
Centre-back Van de Ven transformed into an attacking force to be reckoned with.
Tottenham's first goal came from a cleverly executed corner routine, with Rodrigo Bentancur directing the ball toward the six-yard box for an unmarked Van de Ven to head home.
And Ven de Ven - filling in as captain in Cristian Romero's unavailability - added his next goal in first-half stoppage time as he outjumped the England keeper to nod in.
The Dutchman was just as impressive in defensive duties, combining effectively with Kevin Danso as the duo dealt excellently with the numerous deliveries sent 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 headed to the exits after the midfielder's third for Spurs.
The break in the team's winning streak at home won't be a major worry for David Moyes, but their attacking woes will be.
The forward and the other striker - the Everton's pair of recognised strikers - had scored only a single goal between them before the weekend's outing.
And they were unable to contribute to that poor tally on a wet and gloomy evening on in Liverpool.
The striker's form was epitomized when he opted to bicycle-kick a clear chance from close range, even with having space and opportunity to reposition for a simpler shot that would have challenged Vicario.
The substitute, as well, was unable to influence the game after replacing the starter in the second half.
It wasn't for a lack of chance. Most of the home side's offensive moves came through Grealish and the forward, who relentlessly delivered dangerous balls into the Tottenham box.
Everton: Moyes' men travel to the Stadium of Light in the Premier League on Monday, 3 November at 8 PM.
Spurs: Spurs go to St James' Park on Wednesday, 29 October for their fourth-round League Cup tie against Newcastle.
Liam is a seasoned sports analyst with over a decade of experience in odds modeling and betting strategy.