Micky van de Ven Brace Ends Everton's Run at New Home Ground
The Dutch defender emerged as the initial defender to score twice in a Premier League game for Spurs since the Belgian defender in spring 2013.
Match summary
The Spurs defender heads into the net twice in first half
The home side's defender has goal ruled after VAR review
Senegalese midfielder nets final goal in dying moments
The defeat is Everton's first at Hill Dickinson Stadium
Micky van de Ven scored twice as Spurs prolonged their winning streak in away games in the top division and handed the Toffees their first defeat at Hill Dickinson Stadium.
Everton were unbeaten in their five previous fixtures at their recently opened stadium at Bramley-Moore Dock, having departed their historic home behind after 133 years at the end of the previous campaign.
But Tottenham's leader Van de Ven struck twice from corners in the first half to put their strong form at risk, and they were unable to turn it around before the midfielder - set up by former Toffees attacker Richarlison - nodded in a final goal to put the game to bed.
Jake O'Brien believed he had levelled the tally five minutes after the defender's first goal, directing a powerful header past the Spurs keeper from an Everton corner.
Beto, meanwhile, failed to convert a number of chances, while the Italian goalkeeper made a series of excellent saves to ensure Tottenham went five matches on the road without defeat in the English top flight.
But the video assistant referee stepped in, advising Craig Pawson to check the score on the screen and the official ruled that Jack Grealish and Iliman Ndiaye were in offside positions and had impeded with the Spurs keeper.
This victory elevates Thomas Frank's team into third place in the division, five points off local foes and leaders Arsenal.
Everton remain in 14th position and sit six points ahead of the relegation zone.
Tottenham analysis: The defender excels in role at each end of the field
After a uninspiring midweek display in the European competition against Monaco, where they managed a mere two shots on goal, Frank opted for Randal Kolo Muani in attack instead of former Toffees player the Brazilian.
The summer signing 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.
Centre-back Van de Ven transformed into an offensive threat to be reckoned with.
Spurs' opening strike came from a well-worked corner routine, with the midfielder heading the ball toward the six-yard box for an unmarked the defender to head home.
And the captain - filling in as skipper in the Argentine's unavailability - notched his second in added time as he rose above the England keeper to head home.
Van de Ven was just as impressive in defensive duties, combining well with Kevin Danso as the pair handled superbly with the numerous deliveries sent their way by the opposition.
Everton analysis: Toffees lacking finishing touch
The club's recent stadium had been a fortress, but it appears the novelty may have worn off somewhat and fans headed to the exits after the midfielder's final goal for Tottenham.
The break in the team's unbeaten home run won't be a major worry for the manager, but their attacking woes are.
The forward and the other striker - the Everton's pair of recognised strikers - had netted only a single goal between them before the weekend's outing.
And they were failed to add to that poor record on a wet and gloomy evening on Merseyside.
The striker's performance was epitomized when he chose to bicycle-kick a golden opportunity from close range, despite having space and time to readjust for a more conventional attempt that would have challenged the keeper.
Barry, too, failed to influence the game after coming on for 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 tirelessly whipped threatening crosses into the Tottenham box.
Upcoming fixtures for these two sides?
The Toffees: Moyes' men head to Sunderland in the Premier League on early November at 20:00 GMT.
Spurs: The London club go to Newcastle's ground on Wednesday, 29 October for their next round League Cup match against Newcastle.