The 18-year-old is the youngest woman to compete in the tournament, and has been in dominant form in the PDC Women's Series, but she was unable to land a blow on her Irish opponent.
The crowd were loud in their support of the Doncaster thrower, but O'Connor held his nerve to finish the match with six legs in a row and celebrated the moment magnanimously as he raised Greaves' hand.
Her maiden appearance had started in eye-catching fashion as she nailed a 120 checkout in the opening leg, but she later missed double sixteen to take the set and allowed O'Connor to take the lead.
After nonchalantly checking her phone during the break, Greaves produced another impressive finish of 122 in the second set, and also banked a 180.
But the same pattern unfolded as she faltered at the decisive moment to go 2-0 behind, spurning a chance to go for bullseye and leaving the door open.
O'Connor was ruthless as Greaves' radar wandered in the final set, but with so much time in front of her the teenager is likely to have plenty of better days ahead.
O'Connor suggested the focus on the match had not been to his taste, but predicted Greaves would continue to make waves.
"She threw absolutely brilliant stuff, she has a huge future ahead of her, and hopefully it's the last time I play her for a long time," he said.
"I don't need this attention, I'd rather sneak away in the corner and mind my own business. I wasn't going to fall into the circus of what it was, I just dealt with the task at hand."