Micky van de Ven became the initial backline player to net two goals in a Premier League match for Tottenham since the Belgian defender in spring 2013.
Key points
The Spurs defender heads into the net two times in first half
The home side's defender has equalizer ruled after video check
Senegalese midfielder nets final goal in 89th minute
The defeat is the Merseyside club's first at Hill Dickinson Stadium
Micky van de Ven found the net on two occasions as Spurs extended their unbeaten run on the road in the Premier League and delivered the Toffees their initial loss 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 conclusion of last season.
But Spurs captain the Dutchman struck twice from corners in the opening 45 minutes to place their strong form at jeopardy, and they were failed to mount a comeback before Pape Matar Sarr - assisted by former Toffees attacker the Brazilian - headed home a third to put the game to bed.
The Everton defender thought he had equalized the scores a short while after the defender's first goal, directing a bullet header past the Spurs keeper from an set-piece.
Beto, in the meantime, failed to convert a handful of chances, while Vicario made a succession of fine saves to ensure Tottenham went five away games without defeat in the Premier League.
But the video assistant referee stepped in, instructing the match official to review the score on the screen and the referee ruled that Jack Grealish and Iliman Ndiaye were in an illegal position and had interfered 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 leaders the Gunners.
The Merseyside club stay 14th and are half a dozen points clear of the relegation zone.
After a drab weekday display in the European competition against Monaco, where they mustered a only attempts on target, the manager opted for Randal Kolo Muani up front instead of former Toffees player the Brazilian.
The summer signing was failed to make much of an impact before being substituted for the substitute after 60 minutes on the field, but it turns out he proved unnecessary in the end.
Centre-back the Dutchman transformed into an attacking force to be feared.
Tottenham's first goal came from a cleverly executed set-piece play, with Rodrigo Bentancur directing the ball toward the face of goal for an free the defender to head home.
And the captain - stepping up as skipper in Cristian Romero's unavailability - added his second in first-half stoppage time as he outjumped Jordan Pickford to nod in.
Van de Ven was just as impressive in defence, combining effectively with Kevin Danso as the pair dealt excellently with the 34 crosses sent their way by the opposition.
Everton's new home had been a happy hunting ground, but it seems the novelty may have faded slightly and supporters flocked to the gates after Sarr's final goal for Spurs.
The end in the team's unbeaten home run won't be a massive concern for David Moyes, but their striker situation will be.
The forward and the other striker - the Everton's pair of established strikers - had scored only one league goal combined before Sunday's match.
And they were failed to contribute to that poor record on a damp and dreary evening on in Liverpool.
The striker's performance was epitomized when he chose to bicycle-kick a golden opportunity from close range, even with having space and opportunity to reposition for a more conventional attempt that would have tested Vicario.
The substitute, as well, failed to influence the game after coming on for the starter in the second half.
It wasn't for a lack of chance. The majority of Everton's offensive moves came through Grealish and the forward, who tirelessly whipped threatening crosses into the Tottenham penalty area.
The Toffees: The team head to Sunderland in the top flight on Monday, 3 November at 8 PM.
Spurs: Spurs travel to Newcastle's ground on late October for their next round Carabao Cup tie against the Magpies.
Elara Vance is a digital strategist with over a decade of experience in tech consulting, specializing in helping UK businesses navigate digital transformation and IT innovation.