The Dutch defender emerged as the initial defender to net twice in a English top-flight match for Tottenham since Jan Vertonghen in spring 2013.
Key points
The Spurs defender heads into the net two times in opening period
Everton's defender has goal disallowed after VAR review
Pape Matar Sarr scores final goal in 89th minute
This loss is Everton's first at their new ground
Micky van de Ven found the net on two occasions as Tottenham extended their winning streak in away games in the top division and handed Everton their first defeat at their new home.
Everton were undefeated in their five previous fixtures at their new ground at Bramley-Moore Dock, having left their historic home behind after more than a century at the conclusion of last season.
But Spurs captain Van de Ven pounced twice from set-pieces in the first half to place their impressive record at risk, and they were unable to turn it around before the midfielder - assisted by former Toffees attacker the Brazilian - headed home a third to seal the victory.
The Everton defender thought he had equalized the scores five minutes after Van de Ven's opener, glancing a powerful header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, in the meantime, failed to convert a handful of opportunities, while Vicario made a succession of excellent saves to guarantee the London club went five away games without defeat in the English top flight.
But the VAR intervened, advising Craig Pawson to check the goal on the pitchside monitor and the referee ruled that the winger and Iliman Ndiaye were in offside positions and had impeded with the Tottenham goalkeeper.
The win moves the manager's side up to third in the division, a handful of points off north London rivals and table-toppers the Gunners.
The Merseyside club stay 14th and are half a dozen points clear of the relegation zone.
After a drab midweek performance in the Champions League against Monaco, where they mustered a only two shots on goal, Frank opted for the French striker up front instead of former Toffees player Richarlison.
The new arrival was unable to influence the game before being substituted for the substitute after 60 minutes on the field, but it emerged he proved unnecessary in the end.
Defender the Dutchman transformed into an offensive threat to be feared.
Tottenham's opening strike came from a cleverly executed corner routine, with Rodrigo Bentancur directing the ball toward the face of goal for an unmarked Van de Ven to score.
And Ven de Ven - stepping up as skipper in Cristian Romero's absence - notched his next goal in added time as he outjumped the England keeper to nod in.
Van de Ven was just as outstanding in defensive duties, partnering well with his defensive colleague as the duo dealt superbly with the numerous deliveries thrown their way by the opposition.
Everton's new home had been a happy hunting ground, but it appears the freshness may have worn off slightly and fans flocked to the gates after Sarr's third for Tottenham.
The break in the team's winning streak at home won't be a major worry for David Moyes, but their striker situation are.
Beto and the other striker - the Everton's two established strikers - had netted only one league goal between them before the weekend's outing.
And they were failed to contribute to that miserable tally on a wet and gloomy night on in Liverpool.
Beto's form 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 Vicario.
Barry, as well, failed to influence the game after coming on for the starter in the second half.
It wasn't for a lack of chance. The majority of Everton's offensive moves came through Grealish and Ndiaye, who tirelessly whipped dangerous balls into the Tottenham box.
Everton: The team travel to Sunderland in the top flight on Monday, 3 November at 20:00 GMT.
Tottenham: The London club travel to St James' Park on late October for their fourth-round League Cup match against the Magpies.
Escritora apasionada y viajera incansable, Elena comparte sus experiencias para inspirar a otros en su camino de autodescubrimiento.