Micky van de Ven became the first defender to score twice in a Premier League game for Spurs since Jan Vertonghen in March 2013.
At a glance
Micky Van de Ven heads home twice in opening period
Everton's defender has goal ruled after video check
Pape Matar Sarr scores third in dying moments
The defeat is Everton's initial at their new ground
Micky van de Ven scored twice as Spurs prolonged their unbeaten run on the road in the Premier League and handed the Toffees their initial loss 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 end of last season.
But Tottenham's leader Van de Ven struck twice from corners in the opening 45 minutes to place their impressive record at risk, and they were unable to turn it around before Pape Matar Sarr - set up by former Toffees attacker Richarlison - nodded in a final goal to put the game to bed.
The Everton defender thought he had levelled the tally a short while after Van de Ven's first goal, directing a bullet header past Guglielmo Vicario from an Everton corner.
Beto, in the meantime, failed to convert a handful of opportunities, while the Italian goalkeeper made a succession of fine stops to guarantee the London club went five away games unbeaten in the Premier League.
But the video assistant referee stepped in, advising Craig Pawson to review the goal on the screen and the referee ruled that Jack Grealish and the attacker were in offside positions and had interfered with the Spurs keeper.
This victory elevates Thomas Frank's side into third place in the Premier League, a handful of points off north London rivals and leaders the Gunners.
The Merseyside club remain 14th and sit six points ahead of the drop zone.
After a drab weekday display in the European competition against the French side, where they mustered a mere attempts on goal, the manager opted for Randal Kolo Muani in attack 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 field, but it turns out he proved unnecessary in the end.
Centre-back Van de Ven transformed into an attacking force to be feared.
Spurs' opening strike came from a well-worked corner routine, with Rodrigo Bentancur heading the ball toward the face of goal for an free Van de Ven to head home.
And the captain - filling in as skipper in Cristian Romero's unavailability - notched his next goal in first-half stoppage time as he rose above Jordan Pickford to nod in.
The Dutchman was equally impressive in defensive duties, partnering well with his defensive colleague as the pair handled superbly with the numerous deliveries thrown their way by Everton.
The club's recent stadium 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 won't be a major concern for David Moyes, but their striker situation will be.
Beto and the other striker - the Everton's pair of recognised strikers - had scored only a single goal between them before Sunday's outing.
And they were unable to add to that poor tally on a wet and gloomy evening on in Liverpool.
The striker's performance was summed up when he opted to overhead kick a clear chance from near the goal, even with having space and opportunity to reposition for a simpler attempt that would have tested Vicario.
Barry, as well, failed to make an impact after replacing Beto in the second half.
It wasn't for a shortage of chance. Most of the home side's attacks came through the winger and the forward, who tirelessly whipped threatening balls into the Spurs box.
Everton: The team travel to Sunderland in the Premier League on early November at 8 PM.
Tottenham: The London club travel to St James' Park on Wednesday, 29 October for their fourth-round Carabao Cup tie against the Magpies.
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