Micky van de Ven Brace Ends Everton's Run at Brand New Stadium
The Dutch defender emerged as the first defender to net two goals in a Premier League game for Spurs since Jan Vertonghen in March 2013.
At a glance
The Spurs defender heads into the net two times in opening period
Everton's Jake O'Brien has equalizer ruled after VAR review
Senegalese midfielder scores third in dying moments
This loss is the Merseyside club's first at their new ground
The Tottenham defender found the net twice as Tottenham prolonged their winning streak in away games in the top division and delivered Everton their first defeat at Hill Dickinson Stadium.
The Toffees were undefeated in their last five matches at their recently opened stadium at the dockside location, having left Goodison Park behind after 133 years at the end of the previous campaign.
But Spurs captain Van de Ven pounced twice from corners in the opening 45 minutes to place their impressive record at jeopardy, and they were failed to turn it around before the midfielder - assisted by former Toffees attacker Richarlison - nodded in a third to put the game to bed.
The Everton defender believed he had equalized the scores five minutes after the defender's first goal, directing a powerful header past the Spurs keeper from an set-piece.
The Portuguese striker, meanwhile, failed to convert a number of opportunities, while Vicario made a succession of fine saves to ensure the London club went five away games unbeaten in the English top flight.
But the VAR intervened, advising 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 elevates the manager's side up to third in the Premier League, a handful of points off north London rivals and table-toppers Arsenal.
Everton remain in 14th position and sit half a dozen points ahead of the relegation zone.
Tottenham analysis: The defender excels in role at both ends of pitch
Following a uninspiring midweek performance in the Champions League against the French side, where they managed a mere attempts on target, Frank chose Randal Kolo Muani up front instead of former Toffees player the Brazilian.
The new arrival was failed to influence the game before being replaced for the substitute after an hour on the field, but it emerged he proved unnecessary in the final outcome.
Defender the Dutchman converted into an attacking force to be feared.
Tottenham's first goal came from a well-worked corner routine, with Rodrigo Bentancur heading the ball back across the six-yard box for an unmarked the defender to score.
And the captain - filling in as captain in Cristian Romero's absence - notched his second in first-half stoppage time as he rose above the England keeper to nod in.
Van de Ven was equally impressive in defence, combining effectively with Kevin Danso as the pair handled superbly with the numerous deliveries sent their way by the opposition.
Toffees breakdown: Everton missing striker's instinct
Everton's new home had been a happy hunting ground, but it appears the freshness may have worn off slightly and supporters headed to the gates after Sarr's final goal for Tottenham.
The break in the team's unbeaten home run will not be a massive concern for the manager, but their attacking woes will be.
Beto and the other striker - the Everton's pair of established centre-forwards - had netted only a single goal combined before the weekend's outing.
And they were unable to contribute to that miserable tally on a damp and dreary night on Merseyside.
Beto's performance was epitomized when he chose to overhead kick a golden opportunity from near the goal, despite having space and opportunity to readjust for a simpler shot that would have tested the keeper.
The substitute, too, failed to make an impact after coming on for the starter in the 65th minute.
It wasn't for a lack of chance. Most of the home side's offensive moves came through Grealish and the forward, who relentlessly whipped dangerous crosses into the Tottenham penalty area.
What next for both teams?
Everton: Moyes' men head to Sunderland in the Premier League on early November at 8 PM.
Tottenham: The London club travel to Newcastle's ground on Wednesday, 29 October for their fourth-round Carabao Cup match against the Magpies.