Son Heung-Min broke the deadlock midway through the first half and Kane made it 2-0 in the 47th minute after an excellent run and cross from Son, despite a suspicion of offside.
Harry Kane scored his way to another record.
"You've got to make sure you defend even better against [the likes of] Tottenham when they go 2-0 up and not relinquish that defensive responsibility, otherwise you get what what we just got. I try to keep my goals a bit shorter than that month by month I'll set a target, but who knows what will happen".More news: Watsco Inc (NYSE:WSO) Shares Bought by Stifel Financial Corp
The game will be seen as a must-win by Tottenham fans if they want to keep pace with the top four.
But he is not focusing on future milestones, telling BT Sport: "Four-nil in any game is a great result, Everton are a good side and we played well, we created space and took our chances".
Mauricio Pochettino says that Harry Kane's willingness to improve will see him continue setting goalscoring records on a regular basis. "I'm so happy, it's fantastic because he helps for the win".
"I think a lot of our players were exhausted", Conte added before downplaying the extent of Cahill's injury by saying "I do not think it was serious". I congratulate him, he deserves the credit.More news: Analyst Opinion Summary: American Airlines Group Inc. (AAL), Boise Cascade Company
Everton had the ball in the net first but Wayne Rooney was correctly ruled offside.
"I can't excuse our capitulation after we went 2-0 down". There's still another 44 minutes to play.
"When you look at the number of players who have been brought into this country from overseas - even in the summer - and not worked, particularly up front, it is a risk". "Last week we were very unlucky to get beaten at Liverpool in the last five minutes and this week we got thrashed in the second half".More news: Seal SLAMS Oprah For Weinstein Sexual Assault Knowledge!
"Tottenham can beat anybody by a lot of goals but they should have had to work harder than they did".