Micky van de Ven emerged as the first defender to score twice in a Premier League match for Tottenham since the Belgian defender in March 2013.
Key points
The Spurs defender nods into the net twice in first half
The home side's defender has equalizer disallowed after video check
Senegalese midfielder scores third in 89th minute
The defeat is the Merseyside club's first at Hill Dickinson Stadium
Micky van de Ven scored twice as Spurs prolonged their unbeaten run on the road in the top division and handed Everton their first defeat at Hill Dickinson Stadium.
The Toffees were undefeated in their five previous fixtures at their recently opened stadium at the dockside location, having left Goodison Park behind after 133 years at the conclusion of the previous campaign.
But Spurs captain the Dutchman pounced on two occasions from set-pieces in the first half to place their strong form at jeopardy, and they were failed to mount a comeback before Pape Matar Sarr - set up by former Toffees attacker Richarlison - headed home a third to put the game to bed.
The Everton defender thought he had levelled the scores five minutes after Van de Ven's first goal, directing a powerful header past Guglielmo Vicario from an set-piece.
Beto, meanwhile, missed a number of opportunities, while the Italian goalkeeper made a succession of excellent saves to ensure Tottenham went five away games without defeat in the English top flight.
But the VAR intervened, advising Craig Pawson to review the goal on the pitchside monitor and the official ruled that the winger and the attacker were in offside positions and had impeded with the Spurs keeper.
This victory elevates the manager's side into third place in the division, a handful of points off local foes and table-toppers Arsenal.
The Merseyside club remain 14th and sit half a dozen points ahead of the drop zone.
Following a uninspiring midweek performance in the European competition against the French side, where they managed a only attempts on goal, Frank opted for the French striker up front instead of ex-Everton forward Richarlison.
The new arrival was unable to influence the game before being substituted for Richarlison after an hour on the field, but it turns out he wasn't needed in the final outcome.
Defender Van de Ven transformed into an offensive threat to be feared.
Tottenham's opening strike came from a well-worked set-piece play, with the midfielder directing the ball back across the face of goal for an free the defender to score.
And the captain - stepping up as captain in Cristian Romero's unavailability - notched his next goal in first-half stoppage time as he outjumped the England keeper to nod in.
The Dutchman was just as outstanding in defence, partnering well with Kevin Danso as the duo handled excellently with the numerous deliveries thrown their way by the opposition.
The club's new home had been a happy hunting ground, but it seems the freshness may have faded slightly and fans headed to the gates after the midfielder's final goal for Spurs.
The break in the team's winning streak at home won't be a major worry for the manager, but their attacking woes will be.
The forward and Thierno Barry - the Everton's two established strikers - had netted only one league goal between them before the weekend's match.
And they were unable to contribute to that miserable tally on a damp and dreary evening on Merseyside.
Beto's performance was epitomized when he chose to overhead kick a clear chance from close range, even with having room and opportunity to reposition for a simpler attempt that would have tested Vicario.
The substitute, as well, was unable to make an impact after coming on for the starter in the 65th minute.
It wasn't for a lack of chance. The majority of Everton's offensive moves came through the winger and the forward, who tirelessly whipped threatening crosses into the Spurs box.
The Toffees: Moyes' men head to Sunderland in the Premier League on Monday, 3 November at 8 PM.
Spurs: The London club travel to Newcastle's ground on late October for their next round Carabao Cup tie against Newcastle.
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