In a final made up of two qualifiers, the 23-year-old Diyas broke Kato in the first game before a double fault from the Japanese player at 4-2 allowed the Kazakhstani to serve out for the set.
Diyas broke again in the 11th game of the second set to go up 6-5 before serving out to secure the title.
"It was a tough match and I had to work for every point," Diyas said. "I have been trying to come in more at net to make points shorter and it worked."
On her way to Sunday's final, Diyas dispatched second-seeded Zhang Shuai and defending champion Christina McHale.
Her triumph avenged her disappointment in Japan three years ago, when she lost the final to Samantha Stosur.
The 22-year-old Kato had never reached the quarterfinals at a WTA event before this tournament.