Peterson, the No. 5 overall pick in the April draft, returned a punt 80 yards during the third quarter to put the Cardinals ahead 20-10. Peterson was untouched as he raced up the middle of the field in becoming the fourth player with four punt returns for TDs in a season.
"I just told the guys to be patient, that we'd get one sooner or later," he said.
Rams coach Steve Spagnuolo, who had vowed the rookie wouldn't beat his team again, said after the game that the plan was to avoid kicking it in the middle. But that's exactly what punter Donnie Jones did.
"I mishit it down the middle of the field," Jones said. "So I'll take the blame on that one."
Added Spagnuolo: "We got bit again."
The Associated Press contributed to this report.