The achievement came during her 6-5 second-round victory over Mensur Suljovic at Players Championship 6 in Leicester.
Greaves completed the perfect leg on double 12 and admitted afterwards that the moment took time to sink in.
"I couldn't believe I'd hit it, I just about hit the treble 19, and then I was quite confident that the double 12 was going in," she told the PDC afterwards.
The 21-year-old, competing as a PDC Tour Card holder for the first time in 2026, said she was eager to share the moment with her family.
"I couldn't stop smiling because I couldn't wait to tell my dad, even though I knew he'd be watching it.
"I've narrowly missed hitting one a few times, so it was nice to finally hit one. It's nice to be the first woman to hit one on the PDC ProTour, I'm glad it was on the stream as well."
Greaves opened her campaign with a 6-5 win over Chris Landman before losing 6-3 to David Sharp in the third round.
Reflecting on her start to life on the ProTour, she added: "I'm enjoying my start to life on the PDC ProTour, I've been struggling in patches with a bit of tension in my throw, but I am playing well and enjoying it.
"You're playing the best players in the world, so if you lose a game, it's just a case of your opponent playing better than you on the day."