Price (3-4) didn't allow a walk in notching his fifth career complete game, striking out five in a 98-pitch effort.
It was the left-hander's first home victory in nearly a year, coming in his second start since returning from a six-week stint on the disabled list.
Chicago's John Danks (2-6) absorbed the loss, yielding three runs on five hits over seven full frames. He walked two and fanned five.
Josh Phegley smacked his first career homer for the White Sox.
Notable deaths of 2014 [PHOTOS]
UPI Sports Results for September 19, 2014