The 22-year-old, who won the Doha title in February, had lost previous finals this year at Madrid and Roland Garros, was also a semi-finalist at Wimbledon and quarter-finalist at the Australian Open.
"It's the first WTA tournament organised in Romania and I'm delighted with all my heart to have won it," beamed the 22-year-old.
Halep broke her opponent's serve to open the match and sailed through the first before Vinci, the world number 24, took an early 2-0 lead in the second set.
However, Halep built her offensive behind a solid backhand and came back from an early break down to seal the match with her second match point.
It was Halep's eighth career WTA title.