Micky van de Ven Double Ends Everton's Run at New Home Ground
The Dutch defender emerged as the first defender to net twice in a English top-flight match for Spurs since the Belgian defender in spring 2013.
At a glance
Micky Van de Ven nods home two times in first half
Everton's Jake O'Brien has goal disallowed after video check
Pape Matar Sarr nets third in dying moments
This loss is the Merseyside club's initial at their new ground
Micky van de Ven scored twice as Tottenham extended their unbeaten run on the road in the Premier League and handed the Toffees their initial loss at their new home.
Everton were unbeaten in their five previous fixtures at their new ground at Bramley-Moore Dock, having left Goodison Park behind after more than a century at the end of last season.
But Spurs captain the Dutchman struck twice from set-pieces in the opening 45 minutes to put their strong form at risk, and they were unable to mount a comeback before Pape Matar Sarr - set up by ex-Everton forward Richarlison - nodded in a third to seal the victory.
The Everton defender believed he had equalized the scores five minutes after Van de Ven's opener, directing a bullet header past the Spurs keeper from an Everton corner.
Beto, meanwhile, missed a number of opportunities, while Vicario made a series of excellent saves to guarantee the London club went five matches on the road without defeat in the Premier League.
But the video assistant referee intervened, instructing the match official to check the goal on the screen and the referee ruled that the winger and the attacker were in offside positions and had interfered with the Spurs keeper.
This victory elevates Thomas Frank's side up to third in the division, five points off north London rivals and leaders Arsenal.
Everton stay 14th and are six points ahead of the relegation zone.
Spurs breakdown: The defender fulfils duties at both ends of pitch
After a drab midweek performance in the Champions League against Monaco, where they mustered a mere attempts on goal, Frank chose Randal Kolo Muani up front instead of former Toffees player the Brazilian.
The new arrival was unable to make much of an impact before being replaced for the substitute after 60 minutes on the pitch, but it emerged he proved unnecessary in the final outcome.
Centre-back the Dutchman transformed into an attacking force to be reckoned with.
Tottenham's first goal came from a cleverly executed corner routine, with Rodrigo Bentancur directing the ball back across the six-yard box for an free the defender to score.
And the captain - filling in as skipper in the Argentine's unavailability - notched his second in added time as he outjumped the England keeper to head home.
The Dutchman was equally outstanding in defence, combining well with his defensive colleague as the pair handled excellently with the numerous deliveries thrown their way by the opposition.
Everton analysis: Everton lacking striker's instinct
Everton's new home had been a fortress, but it appears the freshness may have faded somewhat and supporters flocked to the exits 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 striker situation are.
The forward and Thierno Barry - the Everton's pair of recognised strikers - had netted only one league goal combined before Sunday's outing.
And they were failed to contribute to that poor tally on a wet and gloomy night on Merseyside.
Beto's form was summed up when he opted to bicycle-kick a clear chance from near the goal, despite having room and time to reposition for a simpler shot that would have challenged Vicario.
Barry, as well, was unable to make an impact after coming on for the starter in the 65th minute.
It was not for a lack of chance. Most of Everton's attacks came through Grealish and Ndiaye, who relentlessly whipped threatening balls into the Spurs penalty area.
Upcoming fixtures for both teams?
The Toffees: Moyes' men head to Sunderland in the Premier League on Monday, 3 November at 20:00 GMT.
Tottenham: Spurs travel to Newcastle's ground on late October for their fourth-round League Cup match against Newcastle.