Micky van de Ven Brace Halts The Toffees' Run at New Stadium
The Dutch defender became the initial defender to score twice in a English top-flight game for Tottenham since Jan Vertonghen in March 2013.
Match summary
The Spurs defender nods into the net twice in first half
Everton's Jake O'Brien has goal ruled after video check
Senegalese midfielder nets third in dying moments
The defeat is the Merseyside club's first at their new ground
Micky van de Ven found the net on two occasions as Spurs extended their winning streak in away games in the top division and handed the Toffees their initial loss at their new home.
The Toffees were unbeaten in their five previous fixtures at their recently opened stadium at the dockside location, having left Goodison Park behind after more than a century at the conclusion of last season.
But Tottenham's leader Van de Ven struck on two occasions from set-pieces in the first half to put their strong form at jeopardy, and they were unable to turn it around before the midfielder - assisted by former Toffees attacker Richarlison - nodded in a third to put the game to bed.
Jake O'Brien thought he had equalized the tally five minutes after Van de Ven's first goal, directing a bullet header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, meanwhile, missed a handful of chances, while the Italian goalkeeper made a succession of fine stops to guarantee Tottenham went five matches on the road without defeat in the English top flight.
But the VAR intervened, advising Craig Pawson to check the score on the screen and the referee ruled that the winger and the attacker were in offside positions and had interfered with the Tottenham goalkeeper.
This victory elevates the manager's team into third place in the division, five points off north London rivals and table-toppers Arsenal.
Everton remain 14th and are half a dozen points ahead of the drop zone.
Spurs breakdown: Van de Ven fulfils role at both ends of the field
Following a uninspiring midweek display in the European competition against the French side, where they mustered a mere attempts on goal, Frank chose the French striker up front instead of former Toffees player Richarlison.
The summer signing was unable to make much of an impact before being substituted for the substitute after an hour on the pitch, but it emerged he wasn't needed in the final outcome.
Defender 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 face of goal for an free the defender to head home.
And the captain - filling in as skipper in the Argentine's absence - notched his next goal in first-half stoppage time as he outjumped the England keeper to head home.
Van de Ven was just as outstanding in defence, combining effectively with Kevin Danso as the duo dealt superbly with the 34 crosses sent their way by the opposition.
Toffees breakdown: Toffees lacking finishing touch
The club's new home had been a happy hunting ground, but it seems the novelty may have faded somewhat and supporters flocked to the exits after Sarr's final goal for Tottenham.
The end in the team's winning streak at home will not be a massive worry for the manager, but their striker situation are.
The forward and the other striker - the Toffees' two recognised centre-forwards - had netted only a single goal between them before Sunday's match.
And they were unable to add to that miserable tally on a damp and dreary night on in Liverpool.
Beto's performance was summed up when he chose to bicycle-kick a clear chance from near the goal, despite having room and opportunity to readjust for a simpler shot that would have tested Vicario.
The substitute, as well, was unable to influence the game after coming on for Beto in the 65th minute.
It wasn't for a shortage of opportunity. The majority of the home side's offensive moves came through Grealish and Ndiaye, who relentlessly whipped dangerous balls into the Spurs box.
Upcoming fixtures for these two sides?
Everton: The team travel to the Stadium of Light in the Premier League on early November at 20:00 GMT.
Spurs: Spurs travel to Newcastle's ground on Wednesday, 29 October for their next round Carabao Cup match against Newcastle.