Micky van de Ven Double Ends The Toffees' Run at New Home Ground
The Dutch defender emerged as the initial defender to net two goals in a Premier League game for Spurs since the Belgian defender in March 2013.
Match summary
Micky Van de Ven heads into the net two times in opening period
The home side's Jake O'Brien has goal ruled after VAR review
Pape Matar Sarr nets final goal in 89th minute
This loss is the Merseyside club's first at their new ground
Micky van de Ven scored twice as Spurs extended their winning streak on the road in the top division and delivered the Toffees their first defeat at their new home.
The Toffees were undefeated in their five previous fixtures at their new ground at the dockside location, having left Goodison Park 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 place their strong form at risk, and they were unable to mount a comeback before the midfielder - set up by ex-Everton forward the Brazilian - headed home a third to put the game to bed.
Jake O'Brien thought he had levelled the scores a short while after Van de Ven's first goal, glancing a bullet header past the Spurs keeper from an set-piece.
Beto, in the meantime, missed a handful of chances, while Vicario made a succession of excellent saves to ensure Tottenham went five away games without defeat in the English top flight.
But the VAR stepped in, advising the match official to review the goal on the screen and the referee decided that Jack Grealish and Iliman Ndiaye were in offside positions and had interfered with the Spurs keeper.
This victory elevates the manager's side into third place in the division, a handful of points off north London rivals and table-toppers the Gunners.
Everton remain 14th and are six points clear of the relegation zone.
Spurs breakdown: Van de Ven fulfils role at each end of the field
After a drab midweek display in the Champions League against the French side, where they mustered a mere attempts on target, Frank chose Randal Kolo Muani up front instead of former Toffees player the Brazilian.
The new arrival was unable to influence the game before being replaced for Richarlison after 60 minutes on the field, but it turns out he wasn't needed in the final outcome.
Centre-back the Dutchman transformed into an offensive threat to be feared.
Tottenham's opening strike came from a cleverly executed corner routine, with the midfielder directing the ball toward the face of goal for an unmarked Van de Ven to head home.
And Ven de Ven - stepping up as captain in Cristian Romero's unavailability - added his second in added time as he rose above Jordan Pickford to nod in.
The Dutchman was just as impressive in defensive duties, combining well with Kevin Danso as the pair dealt excellently with the numerous deliveries thrown their way by Everton.
Everton analysis: Toffees missing striker's instinct
The club's new home had been a fortress, but it appears the freshness may have worn off slightly and fans flocked to the gates after the midfielder's final goal for Tottenham.
The break in Everton's winning streak at home will not be a major worry for the manager, but their striker situation will be.
The forward and Thierno Barry - the Everton's pair of established centre-forwards - had scored just a single goal combined before Sunday's match.
And they were unable to add to that poor record on a damp and dreary evening on in Liverpool.
The striker's form was summed up when he chose to overhead kick a golden opportunity from near the goal, despite having space and time to reposition for a simpler attempt that would have tested Vicario.
Barry, too, failed to influence the game after coming on for Beto in the second half.
It wasn't for a lack of opportunity. Most of Everton's attacks came through the winger and Ndiaye, who tirelessly whipped threatening crosses into the Spurs box.
What next for both teams?
The Toffees: Moyes' men head to the Stadium of Light in the Premier League on Monday, 3 November at 8 PM.
Spurs: The London club go to St James' Park on late October for their fourth-round League Cup match against the Magpies.