The 22-year-old made a 142 checkout on double 11 in the deciding leg against the former world champion after beating Rob Cross and Gary Anderson, both also former world champions, 6-5 and 7-1 respectively to reach the final.
"Today I played really well. I'm so happy. I cannot even describe the way I feel," said the two-times Women's World Matchplay champion, whose nickname is 'Beau 'n' Arrow'.
"I don't know whether I just thought about being the first woman to win a title but it caught up with me, so I honestly cannot believe I took out that 142.
"I'm beating players I was watching growing up. I'm in disbelief. Now hopefully I can kick on and keep doing it, but it's an amazing feeling."
Greaves was already the first woman to hit a nine-dart finish on the ProTour.