Micky van de Ven Double Ends The Toffees' Run at New Home Ground
The Dutch defender emerged as the first backline player to score two goals in a English top-flight game for Spurs since the Belgian defender in March 2013.
At a glance
The Spurs defender heads into the net two times in first half
Everton's defender has equalizer disallowed after VAR review
Pape Matar Sarr scores third in 89th minute
This loss is the Merseyside club's first at their new ground
The Tottenham defender found the net twice as Tottenham prolonged their unbeaten run in away games in the Premier League and handed Everton their first defeat at their new home.
The Toffees were undefeated in their last five matches at their new ground at Bramley-Moore Dock, having departed Goodison Park behind after 133 years at the conclusion of the previous campaign.
But Spurs captain Van de Ven struck on two occasions from set-pieces in the first half to put their impressive record at risk, and they were unable to mount a comeback before the midfielder - assisted by ex-Everton forward the Brazilian - nodded in a final goal to seal the victory.
The Everton defender thought he had equalized the tally five minutes after the defender's opener, glancing a bullet header past the Spurs keeper from an set-piece.
Beto, meanwhile, failed to convert a number of opportunities, while Vicario made a series of fine saves to ensure Tottenham went five matches on the road without defeat in the English top flight.
But the VAR stepped in, advising Craig Pawson to review the score on the pitchside monitor and the referee decided that the winger and Iliman Ndiaye were in offside positions 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 north London rivals and leaders Arsenal.
Everton stay 14th and sit half a dozen points clear of the relegation zone.
Spurs breakdown: The defender fulfils role at both ends of the field
Following a drab weekday display in the Champions League against Monaco, where they managed a only attempts on target, the manager chose the French striker up front instead of former Toffees player Richarlison.
The new arrival was failed to influence the game before being substituted for Richarlison after an hour on the field, but it turns out he proved unnecessary in the final outcome.
Defender the Dutchman converted into an offensive threat to be feared.
Spurs' opening strike came from a well-worked corner routine, with the midfielder directing the ball toward the six-yard box for an unmarked Van de Ven to score.
And the captain - filling in as skipper in the Argentine's unavailability - notched his next goal in added time as he outjumped Jordan Pickford to nod in.
Van de Ven was equally outstanding in defensive duties, combining effectively with his defensive colleague as the pair handled superbly with the numerous deliveries sent their way by the opposition.
Toffees breakdown: Toffees missing finishing touch
Everton's recent stadium had been a happy hunting ground, but it seems the freshness may have faded somewhat and supporters flocked to the gates after the midfielder's final goal for Tottenham.
The end in Everton's unbeaten home run won't be a major concern for the manager, but their attacking woes are.
The forward and Thierno Barry - the Everton's pair of established centre-forwards - had scored just one league goal combined before Sunday's outing.
And they were failed to contribute to that poor record on a damp and dreary evening on Merseyside.
Beto's form was summed up when he opted to overhead kick a golden opportunity from near the goal, even with having room and opportunity to readjust for a simpler attempt that would have tested Vicario.
The substitute, too, was unable to make an impact after replacing the starter in the second half.
It was not for a lack of chance. The majority of the home side's attacks came through Grealish and Ndiaye, who relentlessly whipped threatening balls into the Spurs box.
What next for both teams?
The Toffees: Moyes' men head to the Stadium of Light in the Premier League on early November at 8 PM.
Tottenham: The London club go to Newcastle's ground on late October for their next round League Cup tie against Newcastle.