Arvidsson held serve at the start of the match, then Frazier won six straight games to earn the first set.
Arvidsson, the 21-year-old Swede, broke at the beginning of the second set to lead 2-0, but Frazier recovered winning the last three games to capture her eighth career singles title.
"In the first set I started out very well and I felt in control," Frazier, a former world number 13, said.
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"I was a little nervous and just tried to keep moving my feet. The second set I think I was a little lucky to get out of. To win any tournament is so exciting. I have really good memories here and I've played good tennis here. So it's such a nice tournament then to win, it's like triple bonus.
"There are moments I don't feel old at all and then sometimes I see the year someone was born and I feel a little older," said Frazier, who becomes the oldest player to capture a WTA Tour singles title in 2005.
Arvidsson was bidding to become the first Swede to capture a Tour singles title since Asa Svensson won at Bol in May 2002.
"I was so nervous, especially in the first set because it was my first final," Arvidsson said.
"She's a tough opponent because she's very consistent and doesn't seem to miss many shots. I started playing better in the second set but she kept fighting. There were a few balls that I should have put in the court and things might have changed if I'd gotten them."
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