Paddy, real name Sarah Patricia Jones and a grandmother of seven, is through to the live semi-finals after Amanda Holden pressed the golden buzzer.
Cowell had already pressed the red buzzer and later said: "I apologise for buzzing a little early before all the crazy things happened - it went ballistic. It was extraordinary."
Judge David Walliams said: "You are an amazing example to older people," before Alesha Dixon added: "I pray to god I am like you when I'm your age, and bravo Nico."
Afterwards Paddy said: "Because I am whizzed round so much I can't see the reaction of people until we have finished the routine."