He threw two scoring passes in the first half, and along with two Nate Kaeding field goals, San Diego led 20-0 at the break. Rivers finished with 18 completions on 30 passes.
Vincent Jackson caught five passes for 142 yards with a touchdown.
Darren Sproles gained 58 yards receiving and 41 rushing, while LaDainian Tomlinson gained a season-high 71 yards on 23 carries for the Chargers (3-3), who snapped a two-game skid.
Kansas City's Matt Cassel was just 10-of-25 passing for 97 yards with a touchdown and three interceptions.
Larry Johnson rushed for 49 yards on 16 carries.
Dwayne Bowe caught a touchdown pass, and Bobby Wade made four receptions for 66 yards for the Chiefs (1-6), whose only victory was last Sunday, 14-6 at Washington.
Celebrity Breakups and divorces of 2014 [PHOTOS]