Niculescu overcame Puchkova 6-2, 4-6, 6-4 in just under 2 hours, improving to 1-2 lifetime in finals.
The 75th-ranked Romanian had lost in the finals at Luxembourg in each of the last two years.
Puchkova had advanced to the title match after surprising top-seeded Venus Williams in Friday's semifinals.
She fell to 0-3 career in championship matches.
Celebrity Families of 2014 [PHOTOS]