It took just one break of serve to settle a tight opening set at the WTA event near San Diego and the second set was no different, Radwanska breaking to take a 5-4 lead before winning the match on the following service game.
Radwanska, the younger sister of world number two Agnieszka, will now meet either Sorana Cirstea of Romania or home hope Sloane Stephens.
US Olympian Varvara Lepchenko eased to a 6-3 6-1 win over American college champion Nicole Gibbs while Alexa Glatch set up a second-round meeting with Russia's Nadia Petrova with a 6-3 6-2 victory over fellow American Lauren Davis.
Rounding off the opening day's action in California, Japan's Misaki Doi beat Michelle Larcher de Brito of Portugal 6-7(6) 6-1 6-3 to set up a date with top seed Marion Bartoli.
At the WTA Swedish Open in Bastad, Mona Barthel got back to winning ways with a 6-3 6-2 victory over Kiki Bertens in the first round.
The German, seeded seventh for the tournament in Sweden, had not recorded a win in five matches previously but made light of her recent form against Dutchwoman Bertens.
Despite a lengthy rain delay midway through the second set, the world number 41 maintained her focus to close out the match without fuss in just over an hour.
"It was a little bit difficult because of the conditions in the beginning; it was really windy and then we had a long break because of the rain," Barthel said.
"I think I played a solid match and played well on the big points, and I'm really happy that I won today because I have lost a lot over the past couple of months.
"For the rest of the tournament, I just want to go out there and have fun and hopefully the results will follow."
Barthel next plays Kateryna Bondarenko of the Ukraine.
In the day's only other match in Bastad, Lesia Tsurenko surprised eighth seed Carla Suarez Navarro 7-5 6-0.
After edging a tight opening set, Ukrainian Tsurenko cantered through the second, serving up a bagel to progress into the second round with ease.
"I wasn't so confident at the beginning of the match, but as the match went on I started playing better and better," Tsurenko said. "Even though I won the first set, I needed that break at the start of the second and this calmed me down.
"The second set was perfect. In fact it was better than perfect! I'm really enjoying playing here and I hope I can continue to play this way for the rest of the tournament."