The Chargers scored 45 unanswered points and Rivers finished 28 of 29 passes for 259 yards and three touchdowns before departing in the fourth quarter.
Rivers broke Mark Brunell's record of 22 straight completions to open a game, set in 2006, set the single-game mark for consecutive completions. Ryan Tannehill completed 25 straight passes for the Dolphins in 2011, but that was over two games.
"(Rivers) had total confidence," wide receiver Keenan Allen said. "He told us before the game he was going to ball out, and that's what he did. He wanted to come back after last week and (have a) bounce back week and I think we did a great job of that."
Running back Melvin Gordon had 10 carries for 61 yards and two touchdowns before leaving with a knee injury in the third quarter as the Chargers (8-3) who rebounded from last week's loss to the Broncos.
Wide receiver Mike Williams scored two touchdowns and Allen caught seven balls for 72 yards and a touchdown -- his third consecutive game with a score.
Rivers has thrown multiple touchdown passes in all 11 games in 2018. Only quarterbacks Johnny Unitas, Peyton Manning and Aaron Rodgers have thrown at least two touchdown passes in their first 11 games to start a season, according to the Chargers.
"He played a tremendous game," Arizona defensive end Chandler Jones said of Rivers. "He took his time, operating that offense. He was picking us apart with those little short passes, those dink passes, and it hurt us. And we missed some tackles on those short passes."
Arizona's Josh Rosen complete 11-of-19 passes for 105 yards, one touchdown and one interception.
One play after a 40-yard Desmond King kick return, Rivers found wide receiver Travis Benjamin for a 27-yard reception. Rivers finished the eight-play drive with a nine-yard touchdown pass to Williams to cut Arizona's lead to 10-7.
The Cardinals recovered a Rivers fumble on a sack, but Dawson's subsequent field goal attempt was wide.
The Chargers next two scores would come from Gordon, on touchdown rushes of 26 and five yards -- the latter set up by Derwin James' interception.
"It's not about how you start, it's how you finish and I feel like we did a great job on the rest of the third downs on the game, getting the offense the ball and getting sacks," James said. "There were plays to be made and we're always making plays."
A Williams two-yard touchdown reception capped a 28-point second quarter for Los Angeles.
Running back Austin Ekeler caught a career high 10 passes for 68 yards and added 35 yards and a touchdown on the ground. Rookie running back Justin Jackson rushed for 57 yards on seven carries.
Los Angeles outscored Arizona 17-0 in the second half.
"I don't think those guys quit," Cardinals coach Steve Wilks said of his team. "I'm not even going to stand up here and say those guys quit. Those guys finished. Do we have to play better? Of course we do."