The US 'I'm Outta Love' singer, who is the latest guest judge on the ITV1 reality show, was moved by the boy's story about his grandmother's cancer.
[Photo gallery - Anastacia at Glasgow auditions]
Copyright: Rex Features Ken Mckay/Thames
Afterwards, Anastacia, who herself has overcome breast cancer, said: "You made this whole audition very special."
She also joined the male singer on stage and met his grandmother after the performance.
The 42-year-old star tweeted today that she had the "best time" as guest judge and has teased fellow judge Gary Barlow, describing the Take That star as "hot".
Speaking before the auditions, Anastacia said: "I didn't sign a record deal until I was 30 and my record label told me to say I was 24. It's never too late to be a popstar."