The Pole is looking to boost her chances of sealing a place at the WTA Finals in Singapore next month, having suffered a second-round exit at the Wuhan Open last week.
And her quest got off to a promising start. After going down an early break in the opening set, Radwanska won four of the next five games to sneak in front.
The 2011 champion was rarely threatened in the second - not facing a single break point - and one break of serve proved enough to seal a comfortable progression to the next round.
Sabine Lisicki had to overcome an early scare against world number 496 Xu Shilin to book a tie against Eugenie Bouchard in the second round with a hard-fought 4-6 6-2 6-0 victory.
The 16-year-old from China claimed the first break and was quick to respond when Lisicki broke back in the sixth game.
However, Lisicki rediscovered her form in the second set to level matters, before seeing out the match in emphatic fashion.
Carla Suarez Navarro of Spain made relatively short work of Belgium's Kirsten Flipkens - picking up a 6-2 6-4 victory.
Suarez Navarro did not look back after breaking in her opponent's opening service game, but was made to battle for the second set as she outnumbered Flipkens by three breaks to two.
The United States' Madison Keys overcame occasional doubles partner Alison Riske 6-3 6-7 (3-7) 7-5 - surviving a match point on her own serve at 5-3 down in the third set.
Elsewhere, world number 152 Romina Oprandi pulled off an upset to beat 39th-ranked Bojana Jovanovski 6-2 6-4, while Kazakhstan's Zarina Diyas eliminated Klara Koukalova of the Czech Republic 6-1 6-4.
Anastasia Pavlyuchenkova was forced to retire from her clash with Zhu Lin at 6-3 3-3 down.