His failure to score had seen him anchored on 99 Spurs goals, but he brought up the century at Goodison Park with a right-wing cross that looped over Jordan Pickford and into the net.
Asked if he meant it, Kane said: "No, I didn't. I think everyone knows or could tell it was a cross so I got a lucky one but sometimes you need that.
"I said that in August, you just need a break to go your way and luckily I got that today then I managed to get the second as well.
"It's been a crazy four or five years so to get that 100th goal is amazing but hopefully now I can get the next 100 even quicker."
Kane took his Tottenham tally to 101 goals after Christian Eriksen had tapped in and the England international hailed a complete performance from Mauricio Pochettino's side.
He said: "It was a very good performance. It's not an easy place to come but we played very well and a 3-0 victory here is very good.
"Everyone on the pitch - from Hugo Lloris all the way through - worked hard and made it difficult for them. The attacking play was fantastic and we scored three good goals.
"We said at half-time we had to try to get the third goal and kill the game. To get it so early on was fantastic.
"It showed just what kind of mentality we've got at the moment. We went in to kill the game, we managed to do that and we're all very happy.
"Everton are a great side and especially with us being away from home as well, we wanted to come here and get a good result.
"We played fantastically, we're very pleased and we want to take this momentum into the Champions League in midweek then next week as well."