On second-and-goal, Dalton pump-faked right and then ran up the middle, dived for the end zone and got the ball across.
The Bengals (7-5) remained tied with Pittsburgh in the race for the AFC's second wild-card berth.
The Chargers (4-8) lost their fourth straight game and for the seventh time in eight games, and remain only mathematically alive in the wild-card chase.
Denver won the AFC West with a 31-23 victory against Tampa Bay.
Philip Rivers had two turnovers in the final 3:54.
Defensive end Carlos Dunlap sacked Rivers, forced a fumble and recovered at the 13 to set up Mike Nugent's 24-yard field goal for a 20-13 lead.
Rivers was then intercepted in the end zone by Reggie Nelson on fourth-and-10 from the Bengals 17 with 49 seconds left.
What are Bolts fans saying about Sunday's game? Find out in the message boards.
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