Rivers only had 128 passing yards but put San Diego ahead on a third-quarter TD pass to Ladarius Green and played mistake-free ball in wet and sloppy conditions as the Chargers scored the game's final 20 points.
Their next stop will be in Denver to face the top-seeded Broncos in the AFC Divisional Round.
Cincinnati quarterback Andy Dalton, however, had much more trouble overcoming the weather, tossing two interceptions and losing a fumble as the Bengals remained in search of their first post-season win since 1991.
The loss was Cincinnati's first at home all season.
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