Mathews finished with 149 yards, including 98 on the ground. His 4-yard run in the third quarter gave San Diego (2-1) a 17-7 lead.
After Kansas City stopped San Diego on fourth-and-inches at the Chiefs 34 with 1:26 to go, Cassel was intercepted by Eric Weddle at the San Diego 49 with 55 seconds left.
Kansas City (0-3) played its first full game without All-Pro Jamaal Charles, who was lost for the season last week with a torn ACL. Dexter McCluster led the Chiefs with 45 rushing yards.
Cassel finished with 176 yards after totaling 256 in his first two games. Dwayne Bowe had 67 receiving yards and a touchdown before leaving in the fourth quarter with an injury.
Despite two more interceptions by Philip Rivers - he has six this season - the Chargers won for the sixth time in the last seven meetings with Kansas City.
The Chiefs were also without tight end Tony Moeaki (preseason) and Pro Bowl safety Eric Berry (Week 1) - they are also out for the season with torn left ACLs.
Chargers Pro Bowl tight end Antonio Gates did not play because of a foot injury.