"I've never been there before," Rams defensive end Chris Long said. "I'm unfamiliar with the sound of it, but I'm liking it."
Bradford finished 7 for 21 for 141 yards, the second-lowest total of his career. He threw for 126 yards against Tampa Bay his rookie year in 2010.
The Rams, ranked 27th in offense, came out throwing, with Bradford completing passes of 14 yards to Brandon Gibson and 44 yards to Amendola on the first two plays, setting up the score to Kendricks on third down. It was the first offensive touchdown in three games for St. Louis.
Arizona responded with a drive that lasted 9:24, ending with Jay Feely's 35-yard field goal. The Cardinals kept the drive alive with three third-down conversions. Larry Fitzgerald's 5-yard catch on the first play of the drive marked his 122nd straight game with a catch, a franchise record.
Zuerlein, a sixth-round draft pick out of Missouri Western, made it 10-3 early in the second quarter. He is 13 for 13 this season, including four kicks of 50-plus yards.
Feely missed a 40-yard field goal late in the second quarter.
Bradford was 3 for 4 for 65 yards on the opening drive before cooling off. St. Louis was well within Zuerlein's range at the Arizona 16 late in the third quarter when Peterson made an interception in the back of the end zone.
Arizona's loss leaves Atlanta and Houston as the only unbeaten teams. The Cardinals were still the St. Louis Cardinals the last time they were 4-0, in 1974. Known as the "Big Red," those Cardinals won their first seven that season en route to a 10-4 record, before losing in the first round of the playoffs to Minnesota.
The loss was only the Cardinals' third in 14 games after starting the 2011 season 1-6.
NOTES: Fitzgerald broke the mark set by Mel Gray from 1973-82 and finished with eight catches for 92 yards, leaving him 48 yards shy of 10,000 for his career. ... Kurt Warner, who took the Rams to two Super Bowls and the Cardinals to one, got a huge sustained ovation when he was introduced in the first quarter. Warner and another former Rams great, Marshall Faulk, are on the NFL Network broadcast team. ... Rams S Quintin Mikell and Cardinals backup LB Reggie Walker were sidelined by blows to the head.