Micky van de Ven emerged as the initial backline player to score twice in a Premier League match for Tottenham since the Belgian defender in March 2013.
Key points
The Spurs defender nods home twice in first half
Everton's defender has equalizer ruled after VAR review
Pape Matar Sarr nets third in dying moments
The defeat is the Merseyside club's first at Hill Dickinson Stadium
Micky van de Ven scored twice as Spurs prolonged their winning streak in away games in the top division and handed Everton their first defeat at their new home.
The Toffees were undefeated in their last five matches at their recently opened stadium at Bramley-Moore Dock, having departed Goodison Park behind after more than a century at the end of the previous campaign.
But Tottenham's leader the Dutchman struck twice from corners in the opening 45 minutes to place their strong form at risk, and they were unable to turn it around before the midfielder - assisted by ex-Everton forward Richarlison - headed home a third to seal the victory.
The Everton defender thought he had levelled the scores a short while after the defender's first goal, glancing a bullet header past Guglielmo Vicario from an Everton corner.
Beto, meanwhile, failed to convert a handful of chances, while Vicario made a succession of fine stops to guarantee the London club went five matches on the road without defeat in the English top flight.
But the video assistant referee intervened, instructing the match official to review the goal on the pitchside monitor and the official decided that Jack Grealish and the attacker were in an illegal position and had impeded with the Spurs keeper.
The win moves the manager's team into third place in the Premier League, a handful of points off local foes and table-toppers Arsenal.
The Merseyside club remain in 14th position and are six points ahead of the drop zone.
After a uninspiring weekday performance in the European competition against the French side, where they managed a only attempts on goal, Frank opted for the French striker in attack instead of ex-Everton forward Richarlison.
The summer signing was failed to make much of an impact before being replaced for the substitute after 60 minutes on the pitch, but it emerged he proved unnecessary in the final outcome.
Defender the Dutchman converted into an attacking force to be reckoned with.
Tottenham's opening strike came from a cleverly executed set-piece play, with Rodrigo Bentancur directing the ball back across the face of goal for an unmarked the defender to head home.
And the captain - stepping up as skipper in Cristian Romero's unavailability - notched his second in added time as he outjumped the England keeper to nod in.
Van de Ven was equally outstanding in defence, combining well with Kevin Danso as the duo dealt superbly with the 34 crosses sent their way by Everton.
Everton's new home had been a fortress, but it seems the novelty may have worn off somewhat and fans headed to the exits after Sarr's final goal for Spurs.
The end in the team's winning streak at home will not be a massive concern for David Moyes, but their striker situation will be.
The forward and Thierno Barry - the Toffees' pair of recognised strikers - had netted only a single goal combined before Sunday's match.
And they were failed to add to that miserable tally on a wet and gloomy night on Merseyside.
The striker's performance was summed up when he chose to bicycle-kick a clear chance from close range, even with having space and opportunity to readjust for a simpler attempt that would have tested the keeper.
Barry, as well, failed to make an impact after coming on for Beto in the 65th minute.
It wasn't for a lack of chance. Most of the home side's attacks came through Grealish and Ndiaye, who relentlessly whipped threatening crosses into the Spurs box.
Everton: Moyes' men travel to the Stadium of Light in the top flight on early November at 8 PM.
Tottenham: The London club travel to St James' Park on late October for their next round Carabao Cup tie against the Magpies.
Elara is a gaming journalist and esports analyst with over a decade of experience covering industry trends and competitive gaming events.