It was the first WTA tour title for the 28-year-old native of Tokyo.
She beat Bartoli on a day the top seed was hampered by a right-hip strain suffered in the pre-match warm-ups.
"Marion hits really well and is very consistent, so today my game plan was to move her around," Morigami said. "Unlike in Seoul last year, I executed my game plan all the way from beginning to the end. Today, I'm glad to say it went my way, but it's very unfortunate for Marion. Hopefully, she will be healthy again soon."
Morigami, who lost two previous matches against her French opponent, collected $21,140.
"I wasn't moving well because of my injury, but sometimes this is how it goes," Bartoli said.