Packers receiver Christian Watson ran for a 46-yard touchdown in the closing minutes after Jaire Alexander intercepted Justin Fields.
Green Bay trailed 19-10 after three quarters but made enough plays down the stretch to come away with its eighth straight win over the Bears.
Rodgers improved to 25-5 against the Bears, including playoffs.
Chicago has lost six straight.
Fields ran for a 56-yard touchdown in the second quarter and finished with 71 yards on six attempts. He was 20 of 25 passing for 254 yards but threw two interceptions.