The striker, who took his tally for the season to 22, helped lift his side above their bitter rivals in the Premier League table on Saturday with a second-half double after Mesut Ozil had put the visitors ahead at White Hart Lane.
A delighted Kane told BT Sport: "What a game, that's probably one of the best we've played all season.
"It was incredible. The fans were incredible, the atmosphere was lightning. They made it better for us.
"That feeling [scoring the winner] was probably one I won't forget for the rest of my career.
"My first London derby and to win the way we did, to dig deep, it's just incredible. I probably won't sleep tonight."
Ozil's opener came after just 11 minutes, but Tottenham's response was impressive and they deserved their leveller, which finally arrived in the 56th minute when Kane calmly volleyed home from a set-piece.
The Englishman's winner came four minutes from time as he climbed to meet Nabil Bentaleb's superb cross.
