The Colts came into the clash in fine recent form and were first to get off the mark, shading a scrappy first quarter thanks to Adam Vinatieri's 30-yard field goal.
From there the Chargers stepped things up to take control in a dominant second quarter, with Rivers finding Keenan Allen on three separate occasions on a sustained drive upfield.
Rivers and Allen combined again soon after for the game's first touchdown, with low dive turning a 74-yard drive into a home score.
San Diego were soon back in touchdown range thanks to variety on offence, but the Colts showed firm resistance to only concede a field goal, which was coolly converted by Nick Novak.
Indianapolis had just under two minutes to respond, but with Andrew Luck let down by receivers the Colts were forced to settle for a 50-yard field goal attempt.
Vinatieri converted from range to keep the Colts close after a tough second quarter, despite their struggles on offence.