Micky van de Ven Double Ends Everton's Run at New Home Ground
The Dutch defender became the first backline player to score two goals in a English top-flight game for Tottenham since the Belgian defender in March 2013.
Match summary
Micky Van de Ven heads into the net twice in opening period
The home side's Jake O'Brien has goal ruled after video check
Pape Matar Sarr nets third in 89th minute
The defeat is the Merseyside club's first at their new ground
Micky van de Ven found the net on two occasions as Tottenham extended their unbeaten run on the road in the top division and handed the Toffees their first defeat at their new home.
The Toffees were unbeaten in their five previous fixtures at their new ground at Bramley-Moore Dock, having departed Goodison Park behind after 133 years at the end of last season.
But Tottenham's leader Van de Ven pounced on two occasions from corners in the first half to place their impressive record at risk, and they were failed to turn it around before Pape Matar Sarr - set up by ex-Everton forward the Brazilian - headed home a final goal to seal the victory.
The Everton defender believed he had levelled the tally five minutes after the defender's opener, glancing a powerful header past the Spurs keeper from an set-piece.
Beto, meanwhile, failed to convert a number of opportunities, while Vicario made a succession of excellent saves to ensure the London club went five away games unbeaten in the Premier League.
But the video assistant referee intervened, instructing the match official to review the goal on the pitchside monitor and the referee ruled that the winger and the attacker were in an illegal position and had impeded with the Spurs keeper.
This victory moves the manager's team into third place in the division, five points off north London rivals and table-toppers the Gunners.
Everton stay 14th and are 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 European competition against the French side, where they mustered a only attempts on target, Frank opted for Randal Kolo Muani in attack instead of ex-Everton forward the Brazilian.
The new arrival was failed to influence the game before being replaced for Richarlison after an hour on the pitch, but it emerged he proved unnecessary in the end.
Centre-back Van de Ven converted into an offensive threat to be feared.
Tottenham's first goal came from a cleverly executed set-piece play, with the midfielder directing the ball back across the six-yard box for an free the defender to score.
And the captain - filling in as captain in Cristian Romero's absence - added his next goal in added time as he rose above Jordan Pickford to head home.
Van de Ven was equally impressive in defence, partnering effectively with his defensive colleague as the duo handled superbly with the 34 crosses thrown their way by Everton.
Toffees breakdown: Toffees lacking striker's instinct
Everton's new home had been a happy hunting ground, but it seems the novelty may have worn off somewhat and fans headed to the exits after the midfielder's final goal for Tottenham.
The end in Everton's unbeaten home run will not be a major worry for David Moyes, but their attacking woes are.
Beto and Thierno Barry - the Everton's two established centre-forwards - had scored only one league goal combined before Sunday's outing.
And they were failed to contribute to that poor tally on a wet and gloomy evening on Merseyside.
Beto's performance was epitomized when he chose to bicycle-kick a clear chance from near the goal, despite having room and time to reposition for a more conventional shot that would have challenged the keeper.
Barry, as well, failed to make an impact after coming on for Beto in the 65th minute.
It was not for a lack of chance. The majority of Everton's attacks came through Grealish and the forward, who relentlessly whipped dangerous balls into the Spurs penalty area.
Upcoming fixtures for both teams?
Everton: Moyes' men head to Sunderland in the top flight on Monday, 3 November at 20:00 GMT.
Tottenham: The London club go to St James' Park on late October for their fourth-round League Cup match against Newcastle.