With the Chiefs trailing 17-6, Cassel fumbled as he was sacked by San Diego's Jarret Johnson in the end zone and Shaun Phillips recovered for a touchdown early in the fourth quarter. On the next drive, Cassel's high pass deflected off Dexter McCluster's hands and was intercepted by Demorrio Williams, who returned it 59 yards for a touchdown.
Williams, who played for the Chiefs the last four seasons, forced a fumble in the first quarter.
The Chiefs had six turnovers in a 37-20 home loss to the Chargers on Sept. 30.
In just 2 minutes, 9 seconds, the Chargers' defense scored as many touchdowns as the offense has in 10 quarters.
Gates' first-quarter score was San Diego's first touchdown since the star tight end caught an 11-yard pass in the first half against Denver on Oct. 15. That score gave San Diego a 24-0 lead, but Peyton Manning rallied the Broncos to a 35-24 win.
The Chargers got only two field goals from Nick Novak in a 7-6 loss at Cleveland on Sunday, their third straight defeat.
After San Diego scored on the opening drive, Kansas City went on a 17-play drive, converting four third downs, but Dwayne Bowe fumbled after a 10-yard reception. Williams caused the fumble and Quentin Jammer recovered.
Bowe's fumble set up Novak's 25-yard field goal with 9:10 left in the second quarter.
After Kansas City decided not to go for it on fourth-and-1 from the San Diego 31, Succop kicked a 49-yard field goal with 2:51 left before halftime.
The Chargers had a third-and-goal from the 1 in the closing seconds of the half when Rivers was intercepted by Eric Berry.
Succop had a 41-yard field goal in the third quarter.