The 35-year-old threw a new F51 European record of 17.68m to score 1100 points and finish ahead of team-mates Josie Pearson and Gemma Prescott.
It beat the previous best of 15.83 set by Ireland's Catherine O'Neill in 2001.
"I'm throwing well at the moment and once I got the big throw, I knew the pressure was off," said Butterfield.
The Glasgow-based newcomer, who was left paralysed by a tumour on her spinal cord in 2011,  took up athletics earlier this year via the talent identification programme Girls4Gold after playing wheelchair rugby for a couple of years.
"Because I was already doing rugby and the strength and conditioning work with that, I just had to try to adapt that to athletics," she told BBC Sport. "I've loved it and trained hard but I know I have a lot more to learn.
"Representing GB for the first time here has been a bit surreal but the team has been great and everyone has been really welcoming.
"The difference sport has made to me is huge but I never dreamed I would be part of this so soon."
Compatriot Pearson was frustrated after three of her six throws were deemed to be fouls.
"There was a technical issue with my throws with an official saying I was breaking some of the rules," she said.
"I've been throwing the same way all season and not been pulled up on it before so it is frustrating for this to happen at a major championship where I know I could have thrown further."
Debutant Jo Butterfield led a British clean sweep of the medals in the women's F32/51 club throw at the IPC Athletics European Championships.