The Chargers spent almost twice as long in possession as their opponents, restricting the Colts to field goals as quarterback Andrew Luck failed to throw a touchdown pass.
Despite that good defensive work when the Colts were in possession, Rivers believes that it was the offensive line who ran the game as he was able to guide his side downfield on a number of long drives.
"We knew if we didn't turn the ball over and we sustained drives, which we did - we had some 12-, 14-, 16-play drives - that we'd give ourselves a chance to win," Rivers told The AP.
"We didn't go into the game saying, 'Let's play ball control'. We wanted to score as many points as we could. We didn't score that many, but we did sustain drives. I thought Keenan Allen stepped up big.
"They were doubling [Antonio Gates] a lot, and Danny Woodhead stepped up big. The offensive line was great. That's the way we need to be able to run the football. If we can mix the run in, we got a chance."
The Chargers are now 3-3 for the season and sit third in the AFC West behind unbeaten duo the Denver Broncos and Kansas City Chiefs.