Radwanska, who received a bye into the second round, saved two set points at 5-4 in the second set before Baltacha saved one match point to force the tiebreaker.
No. 3 ranked and top-seeded Vera Zvonareva of Russia plays her first match at night against U.S. qualifier Jill Craybas, followed by second-seeded Andrea Petkovic, who opens with American Alexa Glatch.
Two seeded players lost as qualifier Marina Erakovic of New Zealand upset No. 14 seed Elena Vesnina of Russia 6-1, 6-2 and Alberta Brianti of Italy was a 1-6, 6-2, 6-2 winner over 10th-seeded Flavia Pennetta of Italy.
No. 11 seed Maria Kirilenko of Russia cruised to a 6-3, 6-2 win over Canada's Rebecca Marino; 12th-seeded Sabine Lisicki of Germany beat Italian Greta Arn 6-0, 6-2; and No. 15 seed Sara Errani of Italy defeated Sania Mirza of India 6-2, 6-3.
Kirilenko did not face a break point on her serve as she hit 75 percent of her first serves. She also took advantage of a back injury Marino suffered in the first set.
Kirilenko, who lost to eventual champion Serena Williams in the quarterfinals last week at Stanford, was rarely pushed by her Canadian opponent.
"I think I played great today," Kirilenko said. "I did everything that we planned. I was happy with that. I tried to mix my game because she is tall."
Both players sought injury treatment at the end of the first set. The Russian saw a trainer for a pain in her left leg, Marino for a lower back injury.
"I did a couple of drop shots and I could see that she was running a little bit (slower)," Kirilenko said.
"I didn't have too much time to adapt because I just came here two days ago," she said. "A little bit different conditions (than last week at Stanford), so I was happy with the way I played."