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: At Least 13 Killed in Southern California Mudslides
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: IED defused by Bomb Squad near Srinagar
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: Senators Say They've Reached Immigration Deal
"Tottenham can beat anybody by a lot of goals but they should have had to work harder than they did".