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The Chargers had the chance to open the scoring to end a scoreless first quarter when Josh Lambo lined up a kick from 42 yards, but he could only send his effort wide of the posts.
Jason Verrett kept the Chiefs from pulling ahead as he made an interception on the goalline by beating Jeremy Maclin to the ball, which ended Chiefs quarterback Alex Smith's streak of 312 passing attempts without a pick.
However, Smith was not deterred by his error as he threw his side into the lead by launching a pass over the Chargers defense for Albert Wilson to collect and race into the endzone.
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Cairo Santos extended his side's lead to 10 points at the break, but the kicker failed in his next attempt early in the second half by sending his effort wide of the posts.
San Diego got on the scoreboard when Philip Rivers engineered a solid drive to take his team into the redzone, and although they were held out of the endzone, Lambo sent his kick through the uprights from 30 yards.
The Chiefs' defense kept the Chargers at bay deep into the fourth quarter, but their offense could not put the game away, giving Rivers one final attempt to bring his side level.
San Diego were thwarted in their attempt to notch a late touchdown despite having several attempts at the endzone, which allowed Andy Reid's men to hold out for the win.
The Chiefs remain the fifth seed in the AFC as the victory improves their record to 8-5, while the Chargers slipped to 3-10 in their campaign.