The clerk had seen Tilian trying to steal two bottles of liquor, then tried to physically restrain him and prevent him from leaving the store, Lincoln police said.
Jones saw what happened, pulled out a handgun and put herself between Tilian and the exit, police said.
Jones has a permit to carry a concealed weapon, police said.
Tilian broke free from the clerk and ran past Jones, exiting the store. Jones shot Tilian as he left the store, hitting him in the back of the arm and missing the store clerk, who also had exited the store, police said.