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.
ATP Rome doubles
Murray enjoys winning return with Broady in Italian Open doubles
"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."
Halep suffers French Open scare as calf tear forces Rome withdrawal against Kerber
Serena suffers shock loss in 1,000th match, Osaka also out