Eva was certainly in a hurry to arrive. Ms Gray was in labour for only three hours, and she just made it to the hospital in time for her second daughter to be born.
Big sister Victoria, 10, was delighted with the new arrival: "She's pretty cool."
Eva weighed in at 6lbs 14oz and was healthy, although weighing considerably less than the Prince who was 8lbs 6oz.
Ms Gray said Eva also shared her birthday with her maternal grandmother.
"My nana, who is no longer with us, was right into the royals and she would have been thrilled to know her great-granddaughter shares a birthday with a prince," Ms Gray said.
She said she would make sure her daughter knew of her connection to the prince, once she was old enough to understand.
"I'm definitely not royal but I think Eva probably is," said Ms Gray with a smile, as she cuddled her newborn.
Statistics New Zealand said about 167 New Zealanders would have been born on the same day as the Prince of Cambridge.