Date Krumm, who turned 40 last month, broke the third-seeded Israeli Peer to go up 6-5 in the third set before serving out for a 3-6, 7-6 (5), 7-5 win.
"Considering my age and the years I was away from the tour, I would say this is a miracle" Date Krumm said. "I just hope that my physical and mental health will last one more game."
The oldest player to win a WTA singles title was Billie Jean King in Birmingham in 1983 when she was 39 years, 7 months and 23 days old.
Date Krumm and Tanasugarn are 1-1 in head-to-head matchups. The Japanese veteran has an 8-6 career record in finals while Tanasugarn is 3-7.