Butterfield, 37, threw 22.81m to take gold, one of eight Britain won in a haul of 21 medals on Sunday.
Two more silvers mean Scottish competitors have now won six medals in GB's current tally of 56.
Cyclist Neil Fachie, in the Tandem B 1000m Time Trial, and para-triathlete Alison Patrick both took silver.
London 2012 gold medallist Fachie, 32, and pilot Pete Mitchell clocked a time of one minute 0.241 seconds, 0.419 seconds behind Tristan Bangma of the Netherlands.
And Dunfermline's Patrick, 28, with Edinburgh guide Hazel Smith, also had to settle for silver in para-triathlon's PT5 category.
Butterfield, a former army civil servant who was paralysed after an operation on a tumour on her spinal cord, initially entered disability sport through wheelchair rugby, and started throwing - the club and the discus - two years ago.
The Glasgow resident added Paralympics gold in the club throw to her 2014 European title and 2015 world title.
"It is a little weird if I am honest, but it's great," she said.
"It is everything I have been working for with my coaches Phil and Shona, so to actually come and nail it is brilliant.
"It has been a tough few days and I must thank my medical team who got me here; it's great to be able to do it for them.
"This is the result of a lot of hard work, but I love what I do. You need a lot of enthusiasm when it is raining in Scotland, to go out and put the time and effort in."
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Scottish medal winners in Paralympics GB team
Gold
Libby Clegg, athletics, 100m T11
Jo Butterfield, athletics, F51 club throw
Silver
Alison Patrick, alongside guide Hazel Smith, para-triathlon PT5
Neil Fachie, along with pilot Pete Mitchell, cycling Tandem B 1000m time trial
Stef Reid, long jump T44
Bronze
Andrew Mullen, swimming 200m freestyle S5
Jo Butterfield became the second Scot to win gold for ParalympicsGB in Rio as she smashed her own world record in the F51 club throw.