Beau Greaves became the first woman to hit a nine-dart finish on the PDC ProTour in February
Beau Greaves narrowly lost 6-5 to Rob Cross on her European Tour debut in the Hungarian Darts Trophy.
The 22-year-old beat Tom Bissell last month to become the first woman to qualify for a PDC European Tour event.
England's Cross won the opening leg in Budapest before Greaves took a 2-1 lead in a thrilling encounter.
They continued exchanging legs as Greaves went 5-4 up to close in on becoming the first women to win a European Tour match.
Requiring 70 to win the match in the deciding leg, Greaves made two poor errors and was punished by Cross.
The narrow defeat continues a remarkable rise after she became the first woman to win a PDC ranking title in April.
Luke Humphries and Michael van Gerwen will enter the tournament in the second round, while world champion Luke Littler is not playing.
