Rivers became just the sixth player to complete 90 per cent of his passes in a single game, connecting on 18 of 20 attempts for 220 yards and a pair of touchdowns that helped the Chargers (4-4) snap a run of three straight defeats.
Rivers hit tight end Antonio Gates in the first quarter and receiver Malcom Floyd in the fourth for his touchdowns.
Rivers said he had his passing rhythm dialled in.
"You definitely feel it," Rivers said. "Playing quarterback in a lot of ways is like a jump shooter, when you get going and you're in a rhythm and you know it.
"It was one of those nights."
The Chargers defense also put points on the board with two fourth-quarter touchdowns.
San Diego's win over their AFC West rivals will give some breathing space to head coach Turner, who came under fire during the Chargers' tailspin, while the Chiefs were left feeling the pressure after a fifth straight defeat.
The Chiefs (1-7) have not had a lead in regulation time in any game this season and their only victory came on an overtime field goal against New Orleans on September 23.
San Diego took the opening kick-off and marched 80-yards for the first score of the game, Rivers hitting Gates with a 14-yard touchdown strike.
Kansas City looked ready to answer right back but fumbled on the San Diego 22-yard line and the Chargers converted the turnover into a 25-yard Nick Novak field goal to lead 10-0.
Ryan Succop got the Chiefs on the scoreboard with a 49-yard field late in the second quarter.
Rivers was on fire in the first half, connecting on 13 straight passes before his first incompletion.
However, after pushing the Chargers to the Kansas City one-yard line in the final seconds of the half, the San Diego quarterback undid much of his good work by throwing an interception in the end zone.
Rivers left the field to a shower of boos despite his near-faultless performance.
"I came out tonight and said, 'Whatever happens I'm stepping up in the pocket on every drop and if I decide to throw it, I'm ripping it,'" said Rivers. "I just ripped one I shouldn't have ripped.
"That was about as good as I can play in a half and that's the loudest I have ever been booed."
Succop connected on a 41-yarder to chop the San Diego lead to 10-6 entering the final quarter.
The Chargers opened the fourth with an 80-yard drive, all of it on the ground, until Rivers hooked up with Floyd on a 13-yard touchdown pass.
In control 17-6, the Chargers defense delivered the knockout punch with a pair of scores, Shaun Phillips jumping on a fumble after Cassel had been stripped of the ball in the end zone.
On the Chiefs' next possession, Demorrio Williams picked off Cassel and returned it 59 yards to cap a 21 point fourth quarter scoring burst for the Chargers.
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