Rodgers compiled 247 yards on 21-of-26 passing, with five completions going to Jordy Nelson, who racked up 105 yards and a score for the Packers (8-0).
Rodgers also found Greg Jennings and Jermichael Finley with scoring passes as Green Bay extended its winning streak to 14 games and continued its best start since 1962.
San Diego's Philip Rivers also threw for four scores, piling up 385 yards on 26-of-46 efficiency, but he was victimized by three interceptions.
Vincent Jackson made seven grabs for 141 yards and three scores as the Chargers (4-4) dropped their third straight.
2014: The Year in Fashion [PHOTOS]
LeBron James reveals his new Nike shoes