It meant it was no surprise when the opener came from the right on 26 minutes when his low cross was finished by Heung-Min Son.
Kane grabbed Spurs' second goal just after the break as he latched on to Heung-min Son's cross, finishing from close range.
That was his 97th Premier League goal - and his 98th came only 12 minutes later as he scuffed a shot into the net from Dier's cross.
With Everton's defence in tatters, Eriksen completed the rout by collecting fellow midfielder Dele Alli's clever flick on before beating Everton goalkeeper Jordan Pickford with a crisp finish in the 81st minute.
They were his 19th and 20th of the season and, with 15 matches left to play, surely the next record in his sights is that of 31 in 38 games, held jointly by Alan Shearer, Christiano Ronaldo and Luis Saurez.
James Ward-Prowse scored his first two goals of the Premier League season for Southampton but that wasn't enough to give the Saints a desperately-needed win as hosts Watford rallied to draw 2-2.
Everton looked to have scored a goal that was ruled out for offside, while Harry Kane's second also looked like the forward was leaning offside.
A quick start to life in the Goodison Park hot seat meant he was on course to ensure just that.
"This way, he's going to break all the records in the Premier League and in England", Pochettino told BT Sport.
Everton will be looking for their first Premier League win of 2018 when they travel to London to face Tottenham Hotspur in match day twenty-three of the Premier League.
This game should be a far more open affair, allowing Tottenham's attack to trouble Everton's defensive frailties.
"I don't know at the moment", Allardyce said.
It is undeniable that this team desperately needs pace but a left-back should be of greater significance, especially after Cuco Martina's latest outing. He has good awareness so it was a very good ball.
Continually using Martina in the position would be foolish in the extreme. Everton will need similar to get anything here.
"You know better than me that if you want to sign players to help you, there must be an opportunity and it's hard to find this opportunity", Pochettino said.
Harry Kane has been linked with a move to Real Madrid in recent months due to his fine form and many believe that this move will go underway either this season or the next one.
Silva has been widely hailed since he arrived in England last season for his work at Hull, which still went down under the Portuguese coach, and Watford.