Chelsea did little to take the spotlight away from under-fire manager Antonio Conte in a goalless draw with Leicester City while Harry Kane broke another record after a brace in Tottenham's 4-0 hammering of Everton.
The goal drew Kane level with Sheringham, but it would soon get even better for the England global.
Spurs responded as Kane tested Pickford with a first-time shot from Moussa Dembele's through-ball on 24 minutes, before they took the lead two minutes later.
Rooney's late booking for an ugly chop on Jan Vertonghen encapsulated Everton's frustration and Tottenham polished off a handsome win with a stunning fourth goal, Dele Alli's lovely back-heel teeing up Eriksen to hammer an emphatic shot past Pickford.
Son was involved in Spur's fourth goal in the 81st.
Everton had the ball in the back of the net after 21 minutes but Wayne Rooney's strike was flagged offside.
Mauricio Pochettino says that Harry Kane's willingness to improve will see him continue setting goalscoring records on a regular basis. We've got to just keep winning games as a team and hopefully I'll keep scoring. 'Hopefully his ability and goalscoring ability will help us along the way, but we've got to get back to the basics defensively like I did when I first started'. He didn't score in the first seven matches of the 2017-18 campaign, but has scored eight goals while adding four assists in the 15 games since.
It was a rotten afternoon for Sam Allardyce at the stadium which should have been his home - but he failed to last long enough as England manager to manage at Wembley. It's him. We work, we talk but in the end, it's always the talent and the belief of the player, to show all they have inside, their talent. "They didn't know if they wanted to play the success story which was a nine and a ten, and then they got confused".
Meanwhile, Bournemouth striker Jermaine Defoe won the Carling Premier League December Goal of the Month award.
"I don't think he would have had this too often at Besiktas where he was left up on his own playing".
He continually powered towards goal whenever he had possession, linking up superbly with Alli and Kane on numerous occasions.
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Eagles finally return to playoff picture
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