Rivers connected with Tolbert on the go-ahead 66-yard scoring play with 45 seconds to go in the first quarter and later tossed a 31-yard touchdown pass to Darren Sproles.
The Chargers' quarterback completed 18-of-25 passes for 373 yards.
LaDainian Tomlinson ran for a 4-yard touchdown, and Nate Kaeding kicked field goals of 32, 42 and 22 yards for San Diego (9-3)
Antonio Gates grabbed eight passes for 167 yards for San Diego, which is atop the AFC West, one game in front of the Denver Broncos, who beat Kansas City 44-13.
Brady Quinn threw three touchdown passes for Cleveland -- one for 11 yards to Mohamed Massaquoi and two 8-yarders to Jerome Harrison.
Quinn was 25-of-45 for 271 yards.
The Browns (1-11) have lost 10 straight contests at home and 17 of 18 overall, going back to last season.