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Jason Myers kicked the home side into a 6-0 lead in the first quarter as he found his range from 22 and 51 yards respectively.
The Chargers rallied to take the lead through Dontrelle Inman when he ran over the middle of the endzone to catch a strike from Rivers.
Myers was called into action for the third time of the match after Blake Bortles had failed to realise he released the ball in front of the line of scrimmage, which nullified a touchdown, although the kicker still put the Jaguars back in front.
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Antonio Gates found the endzone for the Chargers to put the visitors ahead once again as he beat man coverage to catch a nine-yard strike from Rivers.
San Diego pushed further ahead before the break when Bortles threw an interception to Manti Te'o, and Rivers punished his opposite number by lofting the ball to Gates in the endzone.
In the second half, Myers found his range once again by converting his kick from 28 yards after Bortles and his offense stalled in the endzone, but the Chargers restored their 12-point lead through a field goal from Josh Lambo.
Jacksonville brought themselves back into the match in the fourth quarter when Bortles finally got his team into the endzone by connecting with Julius Thomas to come within five points.
However, Rivers ended any hope of a comeback when he notched his fourth touchdown strike of the game by sending a throw high into the arms of the leaping Stevie Johnson.
The Jaguars made the final minute of the match a tense affair when Bortles scored his second touchdown of the game by drilling the ball to Allen Robinson in the endzone on a back-shoulder fade.
Myers attempted an onside kick to keep the game alive, but his kick went out of bounds to allow the Chargers to hold out for the win.