Bencic defeated Wozniacki 6-2 6-4, her fourth win in a row over the former world number one, to reach her fourth WTA final since June.
If the 18-year-old wins, she will break into the world's top 10 rankings for the first time.
"It's amazing to be in the final," she said in her on-court interview.
"Caroline's a great player. If you give free points or aren't focussed enough, she comes back and plays great shots and great tennis.
"So I knew I had to be focussed well from start to finish today. And I was playing some very good games on my serve -- I tried to not let her break me."
Wozniacki was the top seed for the event but had no answer for Bencic, who won her first WTA title at Eastbourne in June then followed up by winning the Canadian Open in August.
"I want to try to win the title now!" Bencic said.
"But I've reached a better result than I ever thought. So I really want to enjoy the final."
Radwanska, chasing her first WTA title in more than a year, joined Bencic in the final with a 6-4 6-1 win over Slovakia's Dominika Cibulkova, who upset Ana Ivanovic to reach the semis but ran out of steam.
Cilbulkova made a strong start, racing to a 4-2 lead, but Radwanska then reeled off 10 of the next 11 games to clinch a straight sets victory.
"I'm just so happy to be in the final here for the third time," said Radwanska, who won the Pan Pacific Open in 2011 and was runner-up in 2012.
"I think this is the only tournament I've been to the final of three times, so it's a special place for me!"
Radwanska lost her only previous meeting with Bencic, in the Eastbourne final, and was expecting another tough encounter with the Swiss teenager.
"I'm ready, but she's definitely on fire," Radwanska said. "She's had a great season, beating pretty much all the top players on the way.
"We played one final on grass, so we'll see how it's going to be on hardcourts, but for sure it's not going to be an easy match. I'll try my best, of course.
"I'll just try to do revenge and we'll see how it goes tomorrow."
(Reporting by Julian Linden in Singapore; editing by Sudipto Ganguly)
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