Investigators say Gillespie slipped into the victim's home through an unlocked sliding-glass back door. Gillespie allegedly attacked the woman as she slept. She screamed and struggled to get free. The suspect fled.
Police say Gillespie ignored orders from police to stop. There was a foot chase, and he was quickly taken into custody.
Gillespie faces seven years to life in prison if convicted.
City News Service contributed to this report.