Karolina Pliskova stormed out to a 4-0 lead in the third set at Olympic Park Tennis Center and held on for the second WTA title of her career in a match that lasted 2 hours, 11 minutes.
Radwanska, ranked fourth in the world and seeking her third title of 2013 after triumphs in Auckland and Sydney, had to battle to subdue her 40th-ranked opponent in two hours and 14 minutes.
American Varvara Lepchenko won in her Fed Cup singles debut to lift the U.S. team to a 1-1 tie against Italy on Saturday, after Sara Errani beat Jamie Hampton 6-2, 6-1.
Serena looked in great touch against Lepchenko, who was never able to trouble Williams after squandering five break points in the opening game.
Saturday's draw pitted Stosur, who said she had left ankle surgery three weeks ago to remove a bone spur, against Sweden's Sofia Arvidsson in the opening round.
Defending US Open champion Samantha Stosur of Australia and Spanish fourth seed David Ferrer advanced at the US Open with straight-set victories on Friday.
Varvara Lepchenko posted a 6-4, 6-2 win over No. 8 seed Chanelle Scheepers of South Africa in the second round of the Mercury Insurance Open on Wednesday.
Defending champion Petra Kvitova wasted little time moving into Wimbledon fourth round as the Czech took just 53 minutes to crush America's Varvara Lepchenko 6-1, 6-0 on Saturday.
On the day Varvara Lepchenko became the last American singles player to exit the French Open, she also learned she's in line to become one of the few Americans to wear the red, white and blue at the Olympics.
Defending champion Li Na of China crashed out of the French Open on Monday, losing a fourth round tie 3-6, 6-2, 6-0 to unseeded Yaroslava Shvedova of Kazakhstan.
Unseeded Varvara Lepchenko of the United States beat 2010 French Open champion Francesca Schiavone of Italy 3-6, 6-3, 8-6 in the third round at Roland Garros on Saturday.
American teen Sloane Stephens advanced to the fourth round at the French Open by beating Mathilde Johansson of France 6-3, 6-2 on Friday.
