The Holland international struck a brace of penalties when the Reds triumphed 2-1 at Goodison back in 2007, beginning the No.18's prolific run of form against the Blues.
Kuyt, who has scored five times against Everton, told the Official LFC Magazine: "In my second year as a Liverpool player, it was a really tough game and the breaks went our way. I remember Rafa read out his list of penalty takers before the game and I was second choice. Andriy Voronin was first on the list.
"When the referee gave the first penalty, Andriy came to me and asked whether I wanted it because he didn't feel too confident. I said: 'No problem...I'll take it.'
"I was so happy to score the first one and when the second one came around, I didn't hesitate. You know that if you miss it, you probably draw the game but it feels like a loss because it's in the last minute.
"To score the winner; it was one of the best feelings I've experienced in my Liverpool career."