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.
Bengals earn stripes in win vs. Bolts
Scout Top Stories
Four Auburn Players Arrested for MarijuanaSophomores Byron Cowart, Carlton Davis III, Ryan Davis and Jeremiah Dinson were arrested at 11 p.m. Saturday night for marijuana possession in the second degree.
ScoutYesterday at 11:37 AM
Tested: 2016 Lexus RX 350 F-SportForm meets function in Lexus' sleek new SUV.
Scout Gear ReviewYesterday at 9:38 AM
Tom Brady's 14-Day Extension Request GrantedTom Brady and his legal team requested a 14-day extension to file an appeal, which was argued against by the NFL, but ultimately approved by the U.S. Court of Appeals.
Patriots Insider2:25 PM
Can Raptors Keep Momentum Against Heat?The Raptors finally got the monkey off their backs by eliminating the Indiana Pacers in 7 games. But can Kyle Lowry and DeMar DeRozan regain their form to beat the Heat?