The win by Radwanska -- her first title since the Rogers Cup in Montreal last year -- helped the seventh-seeded Pole gain revenge for her defeat to the 18-year-old Swiss player in this year's Eastbourne final.
The 26-year-old Radwanska also took the Toray Pan-Pacific in 2011, and is the first player to have won the event twice since it moved outdoors, and onto a hard court, in 2008.
Radwanska, who moves from 13th to eighth in the world rankings with Sunday's title, won eight games in a row to lead 6-2, 4-0.
"This is the first tournament I have won twice, so it's very special for me," said a tearful Radwanska, a Wimbledon semifinalist this year.
In a later news conference, she added: "I really didn't expect that kind of score against Belinda, she's playing so well. I'm never going to be a powerful tennis player, even if I spend the whole day in the gym. That's the way I play, trying to find a way to beat those stronger players.''
Bencic has enjoyed a breakthrough season, winning in Eastbourne and Toronto, including a victory in Canada over Serena Williams in the semifinals.
Bencic also beat top-seeded Caroline Wozniacki in their semifinal on Saturday, and the Swiss player said she was feeling the effects of that match.
"Agnieszka made me run a lot and I think my serves were so slow today because, after yesterday, I couldn't do anything with my legs anymore,'' Bencic said. "In the second set I tried to go for my shots more, even if it meant making more mistakes. I still have a lot to learn to play like her, she's so smart.''