Turner had been heavily criticised by fans after the Chargers blew double-digit, second-half leads in losses to New Orleans and Denver, before going down 7-6 at Cleveland on Sunday.
At the start of halftime, some fans in one end zone unfurled a large banner that read: "Mr. Spanos, please fire A.J. & Norv", making their feelings clear to Dean Spanos, the Chargers' president.
Romeo Crennel, though, will surely feel the heat after his Chiefs side committed four more turnovers and lost their fifth successive game.
Philip Rivers threw a 14-yard touchdown pass to Antonio Gates in the first quarter to open the scoring and flipped a 13-yard touchdown toss to Malcom Floyd early in the fourth quarter to give the Chargers a 17-6 lead with 11:33 remaining.
San Diego then sealed the victory with two defensive touchdowns in a span of only 2:06.
Shaun Phillips, making his 100th NFL start, recovered a fumble in the end zone to stretch the Chargers' lead and Demorrio Williams returned an interception 59 yards for another touchdown to give San Diego a 31-6 edge.
Shaun Draughn ran six yards for a Kansas City touchdown with 4:26 to play but it was too little and far too late.
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