The Chargers (8-6) closed out their regular-season home schedule by winning their second straight and moving within a half game of Kansas City for the lead in the AFC West.
Kansas City will play at St. Louis Sunday, needing a win over the Rams to stay in front in the division race. The Chiefs and Chargers split their two meetings this year and San Diego currently has the tiebreak advantage due to a better conference record than that of Kansas City.
Rivers completed 19-of-25 passes for 273 yards without an interception. He threw scoring passes to Jackson of 58 yards in the first period, 11 yards in the second and 21 in the fourth.
Mike Tolbert added a 1-yard touchdown run for the Chargers in the third period and Nate Kaeding kicked field goals of 25 and 39 yards.
San Francisco's lone touchdown came with 4:26 to play in the game on Brian Westbrook's 3-yard run.
The evening turned bleak for the 49ers after a series of events that cost them a chance to tie the game early in the second quarter.
San Francisco kicked a field goal, but chose to accept a personal foul penalty on the play in hopes of scoring a touchdown. Quarterback Alex Smith appeared to have scored that touchdown on a 7-yard run, but after the play was challenged it was ruled that Smith was pushed out of bounds on the 1-yard line.
The 49ers went for the touchdown on fourth down, only to have Anthony Dixon stopped for a 1-yard loss.
San Francisco fell to 5-9.