Micky van de Ven Brace Ends The Toffees' Run at Brand New Home Ground
The Dutch defender emerged as the first backline player to net two goals in a English top-flight game for Spurs since Jan Vertonghen in March 2013.
At a glance
The Spurs defender heads home twice in opening period
The home side's Jake O'Brien has goal disallowed after video check
Senegalese midfielder scores final goal in dying moments
This loss is the Merseyside club's initial at Hill Dickinson Stadium
Micky van de Ven found the net on two occasions as Tottenham extended their unbeaten run in away games in the top division and handed Everton their initial loss at Hill Dickinson Stadium.
Everton were unbeaten in their last five matches at their new ground at Bramley-Moore Dock, having departed 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 mount a comeback before the midfielder - set up by ex-Everton forward Richarlison - headed home a third to seal the victory.
The Everton defender believed he had equalized the scores five minutes after the defender's opener, glancing a bullet header past the Spurs keeper from an set-piece.
The Portuguese striker, in the meantime, missed a number of chances, while Vicario made a succession of excellent saves to ensure the London club went five away games unbeaten in the English top flight.
But the VAR stepped in, advising Craig Pawson to review the goal on the screen and the official decided that Jack Grealish and the attacker were in an illegal position and had interfered with the Tottenham goalkeeper.
This victory moves the manager's team into third place in the Premier League, five points off north London rivals and leaders Arsenal.
Everton remain 14th and are six points clear of the drop zone.
Spurs breakdown: The defender excels in duties at both ends of the field
After a uninspiring weekday performance in the European competition against Monaco, where they managed a only attempts on goal, the manager opted for the French striker up front instead of ex-Everton forward Richarlison.
The summer signing was unable to influence the game before being substituted for the substitute after an hour on the field, but it turns out he wasn't needed in the final outcome.
Centre-back Van de Ven transformed into an offensive threat to be feared.
Tottenham's opening strike came from a well-worked corner routine, with Rodrigo Bentancur heading the ball back across the six-yard box for an unmarked Van de Ven to score.
And Ven de Ven - filling in as skipper in Cristian Romero's unavailability - added his next goal in added time as he rose above Jordan Pickford to head home.
Van de Ven was equally outstanding in defensive duties, combining well with his defensive colleague as the duo handled superbly with the numerous deliveries thrown their way by the opposition.
Everton analysis: Toffees lacking finishing touch
The club's new home had been a fortress, but it appears the novelty may have worn off somewhat and fans headed to the exits after Sarr's third for Spurs.
The break in the team's unbeaten home run won't be a massive worry for David Moyes, but their striker situation are.
Beto and Thierno Barry - the Everton's pair of recognised strikers - had scored just a single goal between them before the weekend's match.
And they were failed to contribute to that miserable tally on a damp and dreary evening on in Liverpool.
Beto's form was epitomized when he opted to overhead kick a golden opportunity from close range, even with having space and time to reposition for a more conventional shot that would have tested Vicario.
The substitute, as well, failed to make an impact after replacing the starter in the 65th minute.
It was not for a shortage of chance. The majority of Everton's offensive moves came through Grealish and the forward, who tirelessly delivered dangerous balls into the Spurs box.
What next for these two sides?
Everton: Moyes' men travel to Sunderland in the Premier League on Monday, 3 November at 20:00 GMT.
Spurs: Spurs go to Newcastle's ground on Wednesday, 29 October for their next round Carabao Cup tie against Newcastle.