KANSAS CITY, Mo. — The Kansas City Chiefs had relied heavily on their stingy, opportunistic defense during a six-game winning streak that vaulted them right back into playoff contention.

Their defense delivered again on Sunday.

After shutting down San Diego most of the game, the Chiefs forced Philip Rivers into a pair of incomplete passes near the goal line in the final seconds to preserve a 10-3 victory over the Chargers at soggy Arrowhead Stadium that could prove to be critical in the race for an AFC wild card.

“If you’re going to be a good football team, you have to win games like this,” Chiefs coach Andy Reid said. “We found ways to lose games just like this,” referring to last-minute losses to Chicago and Denver during a 1-5 start.

Ever since then, the Chiefs (8-5) have made it nearly impossible to get into the end zone. They held the Chargers without a touchdown when they played three weeks ago in San Diego, then did it again in the most dramatic of fashion on Sunday, with the game on the line as time wound down.

San Diego (3-10) got the ball at its own 11 with 5 minutes left and quickly moved into Kansas City territory, converting fourth down three times. But after Rivers was called for delay of game at the Chiefs 1 with 5 seconds left, he threw high and out of the end zone.

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There was still 2 seconds left, and another incomplete pass that would have ended the game was blown dead for a false start. So with the ball pushed back to the 11-yard line, Rivers scrambled to his right and again threw to the end zone, where his pass to Danny Woodhead skipped incomplete.

“The defense hung tough,” said Alex Smith, who threw a 44-yard touchdown pass to Albert Wilson and finished with 191 yards passing. He also threw his first interception after a franchise-record 312 pass attempts, though that was quickly forgotten in the jubilation of the final seconds.

Playing through the flu, Rivers finished with 263 yards passing and an interception. Melvin Gordon was held to 35 yards rushing in another dismal performance.

“My wife just texted me and said my son said that was the greatest game ever if we’d have won,” Rivers said. “This is the story of our season, losing close games.”

It was evident from the first series that little had changed in the three weeks since the Chiefs shut down Rivers and Co. in a 33-3 win: The Chargers went three-and-out.

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The teams started trading punts throughout the first quarter as rain and wind lashed half-empty Arrowhead Stadium. When the Chiefs got something going, they watched as Frankie Hammond fumbled a punt return. And when the Chargers began to move the ball, penalties shut down their drive.

Kansas City finally took the lead in the second quarter when it began a drive at its own 4-yard line. Eight consecutive running plays netted three first downs, and sucked the entire San Diego defense up to the line of scrimmage. The Chiefs took advantage when Smith hit Albert Wilson on a quick slant route, and he out-ran Steve Williams for a 44-yard touchdown reception.

Rivers was intercepted by Derrick Johnson on the Chargers’ ensuing possession, and Kansas City had just enough time to get within range for of a 40-yard field goal for a 10-0 halftime lead.

The Chargers’ Josh Lambo atoned for an earlier miss with his own 30-yard field goal in the third quarter, but it was the Kansas City defense that starred the rest of the second half.

Dee Ford had his first three sacks of the season in place of injured All-Pro pass rusher Justin Houston, and the defensive backfield managed to blanket San Diego’s wide receivers. Gordon was bottled up all afternoon, and the Chargers were forced to abandon the run game in the final minutes.

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Then, with the game on the line, the Chiefs made two of their biggest stops of the season.

“They just kept on fighting to the very last play there,” embattled Chargers coach Mike McCoy said. “This team has a lot of fight in them. I’m proud of them for that. But this is about winning.”

NOTES: Williams left with a hip injury and did not return. ... Chiefs RB Spencer Ware ran for 52 yards before leaving with bruised ribs. ... Ford finished with a team-high seven tackles. ... The Chiefs sacked Rivers five times. ... Chargers TE Antonio Gates had six catches for 76 yards.