Micky van de Ven Double Ends The Toffees' Run at New Stadium
The Dutch defender became the first backline player to score twice in a English top-flight game for Spurs since the Belgian defender in spring 2013.
At a glance
Micky Van de Ven nods home twice in first half
Everton's Jake O'Brien has equalizer ruled after video check
Pape Matar Sarr nets final goal in 89th minute
This loss is the Merseyside club's first at Hill Dickinson Stadium
The Tottenham defender scored on two occasions as Spurs prolonged their unbeaten run on the road in the top division and delivered Everton their initial loss at their new home.
Everton were unbeaten in their last five matches at their recently opened stadium at Bramley-Moore Dock, having left their historic home behind after 133 years at the end of the previous campaign.
But Tottenham's leader the Dutchman struck twice from corners in the first half to place their impressive record at risk, and they were failed to mount a comeback before the midfielder - assisted by ex-Everton forward Richarlison - headed home a third to put the game to bed.
Jake O'Brien thought he had equalized the tally five minutes after the defender's opener, directing a bullet header past Guglielmo Vicario from an Everton corner.
Beto, in the meantime, failed to convert a handful of chances, while the Italian goalkeeper made a series of excellent saves to ensure the London club went five matches on the road unbeaten in the Premier League.
But the VAR intervened, instructing Craig Pawson to review the score on the pitchside monitor and the referee ruled that Jack Grealish and Iliman Ndiaye were in offside positions and had interfered with the Tottenham goalkeeper.
The win moves the manager's side into third place in the Premier League, five points off local foes and leaders Arsenal.
The Merseyside club stay 14th and sit six points ahead of the drop zone.
Spurs breakdown: Van de Ven excels in role at both ends of pitch
After a drab midweek display in the European competition against the French side, where they managed a only attempts on target, Frank opted for the French striker up front instead of ex-Everton forward Richarlison.
The new arrival was failed to make much of an impact before being replaced for Richarlison after 60 minutes on the pitch, but it emerged he proved unnecessary in the end.
Centre-back the Dutchman transformed into an offensive threat to be reckoned with.
Spurs' first goal came from a cleverly executed corner routine, with the midfielder heading the ball back across the six-yard box for an free Van de Ven to score.
And the captain - filling in as captain in Cristian Romero's absence - notched his second in first-half stoppage time as he rose above the England keeper to head home.
The Dutchman was equally outstanding in defence, partnering effectively with his defensive colleague as the duo handled excellently with the numerous deliveries sent their way by Everton.
Toffees breakdown: Toffees missing striker's instinct
The club's new home had been a fortress, but it seems the freshness may have worn off somewhat and fans flocked to the gates after Sarr's final goal for Spurs.
The end in the team's winning streak at home will not be a massive worry for David Moyes, but their attacking woes are.
The forward and Thierno Barry - the Toffees' pair of established centre-forwards - had scored only a single goal between them before Sunday's outing.
And they were unable to add to that miserable record on a damp and dreary night on Merseyside.
Beto's performance was summed up when he opted to overhead kick a golden opportunity from close range, even with having room and opportunity to reposition for a simpler attempt that would have tested the keeper.
The substitute, as well, failed to make an impact after coming on for the starter in the 65th minute.
It was not for a lack of opportunity. The majority of Everton's attacks came through Grealish and Ndiaye, who tirelessly delivered threatening crosses into the Tottenham penalty area.
Upcoming fixtures for these two sides?
The Toffees: Moyes' men head to the Stadium of Light in the Premier League on Monday, 3 November at 20:00 GMT.
Spurs: Spurs go to Newcastle's ground on late October for their next round Carabao Cup match against the Magpies.