On second-and-goal, Dalton pump-faked right and then ran up the middle, dived for the end zone and got the ball across for a 17-13 lead.
The Bengals (7-5) remained tied with Pittsburgh in the race for the AFC's second wild-card berth.
The Steelers and Bengals are two games behind the AFC North-leading Baltimore Ravens, who lost to Pittsburgh.
The Chargers were shut out in the second half after taking a 13-10 halftime lead.
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.
On the first Chargers' possession after Dalton's TD, 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.
The Bengals overcame three turnovers, including two interceptions by Dalton. One of them was returned 31 yards for a touchdown by Demorrio Williams.
The Bengals took the game's opening kickoff and moved 91 yards, capped by Dalton's 19-yard pass to tight end Jermaine Gresham for a 7-0 lead.
Dalton threw an incompletion on fourth-and-9 from the Chargers 35, but Chargers cornerback Shareece Wright was called for holding and the drive continued at the San Diego 30.
The Chargers had a nice drive of their own and had a first-and-goal from the Bengals 7.
But Rivers fumbled when he was hit going back to pass. Tight end Antonio Gates recovered at the 16. The Chargers reached the 2-yard line but had to take Nick Novak's 20-yard field goal that pulled them to 7-3.
Two plays into the next Bengals drive, Williams intercepted Dalton and returned it 31 yards down the left sideline to give the Chargers a 10-7 lead. It was Williams' second interception returned for a touchdown this season.
The Bengals drove deep on the Chargers again and had a first-and-goal on the 5. A.J. Green was wide open in the end zone but Dalton overthrew him. BenJarvus Green-Ellis gained 4 yards to the 1, but an incomplete pass forced the Bengals to settle for Nugent's 19-yard field goal and a 10-10 tie.
San Diego made it to the Bengals 1 with a second before halftime and had to settle for Novak's 19-yard field goal for a 13-10 lead.