It was the 17-year-old Konjuh's third match in two days after playing both her quarterfinal and semifinal on Sunday.
Fatigue could have accounted for Konjuh dropping her first set of the week. But the 61st-ranked Niculescu dropped her serve early in the second set to fall 3-0 behind and the 27-year-old Romanian never recovered.
''I didn't expect it,'' the 87th-ranked Konjuh said. ''I came here two days before to acclimatize on grass, and after five matches I've won the tournament, so it feels great.
''The first set wasn't going my way but I had to stay calm. I just knew that my game was going to come and I did it much better in the second set.''
Konjuh has previously won the junior titles at the Australian and U.S. Opens.