Micky van de Ven became the initial backline player to net two goals in a Premier League match for Spurs since the Belgian defender in spring 2013.
Key points
The Spurs defender nods into the net twice in first half
Everton's defender has equalizer ruled after VAR review
Senegalese midfielder scores third in 89th minute
This loss is Everton's initial at Hill Dickinson Stadium
The Tottenham defender found the net twice as Tottenham prolonged their unbeaten run in away games in the Premier League and handed the Toffees their initial loss at Hill Dickinson Stadium.
The Toffees were unbeaten in their last five matches at their new ground at Bramley-Moore Dock, having departed Goodison Park behind after more than a century at the end of last season.
But Tottenham's leader the Dutchman pounced twice from corners in the first half to put their strong form at jeopardy, and they were failed to turn it around before the midfielder - assisted by former Toffees attacker Richarlison - headed home a third to seal the victory.
The Everton defender thought he had equalized the tally a short while after the defender's opener, glancing a bullet header past Guglielmo Vicario from an Everton corner.
Beto, meanwhile, failed to convert a number of chances, while Vicario made a series of fine stops to ensure the London club went five away games without defeat in the Premier League.
But the VAR intervened, instructing the match official to review the goal on the screen and the referee ruled that Jack Grealish and Iliman Ndiaye were in offside positions and had interfered with the Spurs keeper.
This victory moves Thomas Frank's team into third place in the Premier League, five points off north London rivals and leaders Arsenal.
The Merseyside club remain in 14th position and sit six points ahead of the drop zone.
Following a drab weekday performance in the Champions League against the French side, where they mustered a mere attempts on target, Frank chose Randal Kolo Muani in attack instead of former Toffees player the Brazilian.
The summer signing was failed to make much of an impact before being replaced for Richarlison after 60 minutes 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.
Spurs' opening strike came from a cleverly executed corner routine, with the midfielder directing the ball back across the face of goal for an free the defender to score.
And the captain - stepping up as captain in Cristian Romero's absence - notched his second in first-half stoppage time as he outjumped Jordan Pickford to nod in.
The Dutchman was just as outstanding in defence, combining effectively with his defensive colleague as the pair handled superbly with the numerous deliveries sent their way by Everton.
The club's recent stadium had been a happy hunting ground, but it seems the novelty may have worn off somewhat and supporters headed to the exits after the midfielder's final goal for Spurs.
The end in the team's winning streak at home will not be a major concern for the manager, but their attacking woes will be.
Beto and the other striker - the Toffees' two recognised strikers - had scored just a single goal between them before the weekend's match.
And they were failed to add to that poor record on a wet and gloomy evening on in Liverpool.
Beto's performance was epitomized when he opted to overhead kick a clear chance from close range, despite having room and opportunity to reposition for a more conventional shot that would have tested the keeper.
Barry, as well, was unable to make an impact after coming on for the starter in the second half.
It wasn't for a shortage of opportunity. The majority of the home side's offensive moves came through the winger and the forward, who relentlessly delivered threatening crosses into the Tottenham penalty area.
Everton: The team travel to Sunderland in the Premier League on Monday, 3 November at 20:00 GMT.
Tottenham: The London club go to St James' Park on late October for their fourth-round Carabao Cup match against Newcastle.
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