Kirilenko was leading the third-seeded Schiavone 6-1, 1-2 in the second round when the Italian, who had taken a medical time-out in the first set with an apparent right thigh injury, retired.
Kirilenko will next play seventh-seeded Vera Dushevina of Russia, who beat Anastasija Sevastova of Latvia 7-5, 6-1.
Top-seeded Daniela Hantuchova of Slovakia also advanced, defeating Chanelle Scheepers of South Africa 6-1, 6-1.
Hantuchova, who did not face a break point, will next face Kimiko Date Krumm of Japan, who saved a match point before eliminating fifth-seeded Alisa Kleybanova of Russia 4-6, 7-6 (4), 6-3.
"I don't have any problem in my physical stamina," the 39-year-old Date Krumm said. "I'll also do my best in the next match."