His charity Medicine Mondiale started a $2 million global fundraising appeal to get the Life Pod device into production for Third World hospitals.
Sir Ray, who emigrated to New Zealand in 1973, developed an interest in science at the age of 14 when he was living rough in London, a fact documented in his 2010 autobiography Rebel with a Cause.
Grace's mum Penelope Robinson said she was extremely proud of her daughter for donating her pocket money and the genuine letter which attracted an immediate response from Sir Ray.
"Ray wrote her a gorgeous letter and answered her question. He used to ask a lady that worked in the local bakery if he could have any stale buns that they were going to throw away and they took pity on him."
Grace, who attends Edendale Primary School in Sandringham, said the response from her hero, which came with a signed copy of his book, was an unexpected thrill.
"I was very delighted because I was sick that day so it made my day definitely."
Grace, who was diagnosed with coeliac disease this year following months of stomach pains, said because of Sir Ray she wanted a career helping people when she grew up.
"I want to help people, maybe save lives, that's what I would like to do.
"I don't know if that's a scientist or doctor, I'm not sure."
The pair met yesterday for the first time and Sir Ray said Grace was a wonderful example of the spirit of the incubator campaign: "Keep little hearts beating."
"Often every day I'm confronted with the juxtaposition between the way our society is flawed and that we don't look after each other properly, particularly on a global scale.
"So Grace exemplifies the way we should be as a society."
Sir Ray said Grace gave him "great hope" for the future generation and inspired him because of her thoughtfulness at a time when her own health was poor.
"She's had a pretty tough year ... and to think of others when things are going on in your life that are not really good is inspirational."
Life savers
• Life Pod incubators cost about $2550 and a conventional incubator around $45,000.
• They can purify their own air and water and run for 10 years.
• Each unit has the potential to save up to 500 babies