The Bears scored the first 20 points and then held on despite being outgained 383 yards to 185.
San Diego quarterback Philip Rivers threw an interception and the Chargers lost three fumbles to slow down the offense.
Matt Forte added a 3-yard touchdown run in the first period for the Bears and Gould was good on field goal attempts of 23, 25, 28 and 48 yards.
Rivers was 5-of-9 for 50 yards.
Chicago improved to 1-1 in exhibition play. San Diego has lost both its games.
2014: The Year in Fashion [PHOTOS]
UPI Sports Results for September 19, 2014