The Bengals (8-4), coming off their bye, kept a two-game lead over Baltimore.
San Diego (5-7) lost the momentum it gained with a thrilling comeback win at Kansas City a week earlier and saw its playoff hopes dwindle after its fourth loss in five games.
On the Bengals' next drive, Andrew Hawkins caught a short pass from Dalton on third-and-2 from the Bengals 18 and raced 50 yards to the San Diego 32, where he was pushed out of bounds. The Bengals settled for Mike Nugent's 46-yard field goal for a 17-7 lead.
The Bengals appeared to be driving for a score that would have put away the game, but BenJarvus Green-Ellis fumbled when he was hit by Gilchrist.
Weddle recovered and returned it 27 yards to the San Diego 43. The drive stalled and Nick Novak kicked a 48-yard field goal to pull to 17-10 with 4:43 left.
Green-Ellis gained 92 yards on 20 carries.
The Bengals held Philip Rivers to 252 yards passing and have allowed only one 300-yard passing day by an opponent this season.
Dalton was 14 of 23 for 190 yards.
Cincinnati's offensive line manhandled the Chargers on the Bengals' second drive, which ended with BenJarvus Green-Ellis scoring on a 4-yard run.
The Chargers responded with a long drive capped when second-year tight end Ladarius Green split linebackers Rey Maualuga and Vontaze Burfict and was wide open for a 30-yard touchdown reception to tie the game at 7.