Williams maintained her perfect record over Radwanska, her six wins over the world number four from Poland including a triumph in the 2012 Wimbledon final and, more recently, in the semi-finals at Miami this year.
Williams next faces unseeded Romanian Cirstea, who toppled fourth-seeded Li Na of China 6-1, 7-6 (5).
The victory over 2011 French Open champion Li continued a dream run for 27th-ranked Cirstea in the $2.4 million hardcourt tournament.
She also beat former world number ones Caroline Wozniacki and Jelena Jankovic, as well as defending champion Petra Kvitova, en route to the final.
“Gosh, she hits really hard,” Williams said of Cirstea. “She has a really big serve. She moves well, she’s definitely not an easy player to play.
“She is a player who has finally found herself, and she’s playing better and better and getting more confident.”
Williams found herself in a tight battle against Radwanska, twice recovering a break in the opening set before holding to force the tiebreaker.
She took control early in the tiebreaker, taking a 3-1 lead, and gave herself a triple set point with a cross-court winner for 6-3.
She needed just one of those set points, firing an ace to seal the set.
But Williams was clearly frustrated as she again went down a break to trail 3-1 in the second.
Once again, however, Williams rallied. After a medical timeout because of a stomach ailment, she regained the break to level the set at 3-3 with a fierce overhead winner to end a long rally on her third break chance.
Williams then saved a break point to hold for a 5-4 lead, and broke Radwanska in the last game with a backhand winner followed by a high forehand volley on match point to seal the victory in one hour and 51 minutes.
“So, well, next time,” Radwanska said.
Cirstea was looking forward to her shot at Williams.