Everton gave a debut to new £27m signing, Cenk Tosun, but the former Besiktas striker had little to work with as the ninth-placed Blues, who saw a header from Wayne Rooney correctly chalked off for offside, slumped to a fourth straight defeat.
The impressive Son Heung-Min had opened the scoring in the first-half as he notched for a fifth straight home league match, while Christian Eriksen put the seal on an emphatic success when he finished off a wonderful move nine minutes from time.
Harry Kane is 10/3 to score and assist against Everton.
Tottenham are now fifth in the league table with 41 points from 22 matches, three points behind fourth-placed Liverpool.
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Spurs snatched their deserved lead four minutes later, when Son tapped in for his eighth goal of the season.
Everton now sit ninth in the division but they have been woeful away from home having taken just 8 points from a possible 27 on the road so far this campaign.
The Blues have not won away at Tottenham since 2008 but will swap the regular trip to the confines of White Hart Lane for the national stadium as they look to grab a result against Mauricio Pochettino's side.
Kane has now scored 20 league goals this season, three more than the next most prolific, Liverpool's Mohamed Salah.
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Watford came back from two goals down to register a 2-2 draw with Southampton at Vicarage Road.
Spurs were rampant, though, and just a minute later they had their third goal as Kane surpassed Sheringham as Tottenham's highest-ever Premier League goalscorer, bringing up number 98 with another close-range finish, although this one was scuffed over Pickford from Eric Dier's drilled low delivery.
Son was involved again as Alli had a chance to make it three with 53 minutes played but could only steer his attempted finish into the side netting.
Manchester City boss Pep Guardiola was named December's Premier League manager of the month for a record fourth consecutive time, while Tottenham Hotspur striker Harry Kane equalled Steven Gerrard's tally with his sixth player of the month award.
Walcott: Allardyce confirms Everton pursuit of Arsenal man
We have a good relationship with Theo, and I don't want him to be frustrated or lose an opportunity to go the World Cup. He said: "We'll see". "If that can be sorted out it would be a great addition from an attacking point of view".
Everton didn't notch a single shot on goal in the first half, part of a disconcerting trend for the club.