Chargers 31
Chiefs 13

SAN DIEGO — Norv Turner can breathe a little easier after his San Diego Chargers rediscovered the end zone and ended a three-game losing streak.

Romeo Crennel, though, will surely feel the heat after his Kansas City Chiefs committed four more turnovers and lost their fifth straight game.

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Antonio Gates caught a 14-yard scoring pass from Philip Rivers on the game’s opening drive to snap a streak of six quarters without a touchdown, and the Chargers went on to a 31-13 win over the Chiefs Thursday night.

Turner had been criticized by fans after the Chargers (4-4) blew double-digit, second-half leads in losses to New Orleans and Denver, and then lost, 7-6, at Cleveland last Sunday.

Rivers completed 18 of 20 passes — a career-best 90 percent — for 220 yards and two touchdowns, with one interception. Rivers also threw a 13-yard TD pass to Malcom Floyd early in the fourth quarter. It was the sixth time in NFL history a quarterback had completed 90 percent or more of his passes.

‘‘It was good to play well but more importantly, it was good to win a game. We needed a win in the worst way,’’ Rivers said. ‘‘Games like this, wins like this, can jump-start us.’’

The Chiefs (1-7) committed four more turnovers and lost their fifth straight game. Running back Jamaal Charles left with a neck injury in the fourth quarter.

The Chiefs’ four turnovers ran their NFL-high mark to a staggering 29, which have led to 104 points. The Chiefs still haven’t led in regulation this season. Their only victory came when Ryan Succop kicked the winning field goal against the Saints in overtime.

With the Chiefs trailing, 17-6, Matt 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.