Greaves defeated Michael Smith 8-7 in the Players Championship 11 final in Milton Keynes.
The 22-year-old completed the victory with an impressive 142 check-out.
Greaves beat three former world champions in the tournament, dispatching Smith, Rob Cross and Gary Anderson.
"I can't believe it. I don't know whether I thought about being the first woman to do one. I can't believe I've hit that," she said.
"I've had a great year, but I never thought I'd win one of these."
Greaves is a rising star after amassing a 114-match winning run in the PDC Women's Series.
She also became the first woman to hit a nine-dart finish on the PDC ProTour.
Greaves had surprised even herself with a 7-1 rout of two-time world champion Anderson in the semi-finals in Milton Keynes.
"I know I've got the ability and the talent, but I've beaten Gary Anderson and I couldn't believe it! Beating Michael. Beating players that I watched growing up," she said.
"It's amazing and I feel really proud of myself."