Micky van de Ven Double Ends Everton's Run at Brand New Stadium
The Dutch defender became the first defender to net twice in a Premier League match for Tottenham since the Belgian defender in March 2013.
Match summary
Micky Van de Ven heads home twice in first half
Everton's Jake O'Brien has goal disallowed after video check
Senegalese midfielder nets final goal in dying moments
This loss is the Merseyside club's initial at Hill Dickinson Stadium
The Tottenham defender found the net twice as Spurs extended their winning streak on the road in the top division and delivered the Toffees their first defeat at Hill Dickinson Stadium.
Everton were unbeaten in their last five matches 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 Tottenham's leader Van de Ven pounced twice from corners in the first half to place their strong form at jeopardy, and they were unable to mount a comeback before Pape Matar Sarr - assisted by ex-Everton forward the Brazilian - headed home a third to seal the victory.
Jake O'Brien believed he had equalized the tally five minutes after the defender's opener, glancing a bullet header past Guglielmo Vicario from an Everton corner.
The Portuguese striker, meanwhile, missed a handful of opportunities, while the Italian goalkeeper made a series of fine saves to ensure the London club went five matches on the road without defeat in the English top flight.
But the VAR intervened, instructing 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.
The win elevates the manager's team up to third in the Premier League, five points off north London rivals and table-toppers the Gunners.
Everton stay in 14th position and are six points ahead of the relegation zone.
Tottenham analysis: The defender excels in role at each end of the field
Following a drab midweek display in the European competition against Monaco, where they managed a only attempts on goal, Frank chose the French striker in attack instead of ex-Everton forward the Brazilian.
The new arrival was unable to make much of an impact before being replaced for Richarlison after 60 minutes on the field, but it emerged he proved unnecessary in the end.
Defender Van de Ven transformed into an offensive threat to be feared.
Spurs' opening strike came from a cleverly executed corner routine, with Rodrigo Bentancur heading the ball back across the face of goal for an unmarked Van de Ven to score.
And Ven de Ven - stepping up as captain in Cristian Romero's unavailability - notched his next goal in added time as he rose above Jordan Pickford to nod in.
Van de Ven was just as impressive in defensive duties, combining effectively with Kevin Danso as the duo handled superbly with the 34 crosses thrown their way by Everton.
Toffees breakdown: Toffees lacking finishing touch
The club's recent stadium had been a fortress, but it appears the freshness may have worn off slightly and fans headed to the gates after the midfielder's third for Tottenham.
The break in Everton's unbeaten home run will not be a massive concern for the manager, but their attacking woes are.
Beto and Thierno Barry - the Toffees' two established centre-forwards - had scored only a single goal combined before Sunday's match.
And they were unable to contribute to that poor tally on a wet and gloomy night on in Liverpool.
The striker's performance was summed up when he chose to overhead kick a golden opportunity from close range, even with having room and opportunity to readjust for a more conventional shot that would have challenged the keeper.
Barry, as well, was unable to influence the game after coming on for Beto in the 65th minute.
It was not for a lack of chance. Most of Everton's attacks came through the winger and the forward, who tirelessly whipped dangerous crosses into the Spurs penalty area.
Upcoming fixtures for both teams?
The Toffees: The team travel to Sunderland in the Premier League on Monday, 3 November at 8 PM.
Tottenham: The London club travel to Newcastle's ground on late October for their next round Carabao Cup tie against the Magpies.